Algebra 2B
An air show is scheduled for an airport located on a coordinate system measured in miles. The air traffic controllers have closed the airspace, modeled by a quadratic equation, to non-air show traffic. The boundary of the closed airspace starts at the vertex at (10, 6) and passes through the point (12, 7). A commuter jet has filed a flight plan that takes it along a linear path from (-18, 14) to (16, -13). Which system of equations can be used to determine whether the commuter jet's flight path intersects the closed airspace?
A
Graham and Hunter are circus performers. A cable lifts Graham into the air at a constant speed of 1.5 ft/s. When Graham's arms are 18 ft above the ground, Hunter, who is standing directly underneath Graham, throws Graham a ball as the cable continues to lift him higher. Hunter throws the ball from a position 5 ft above the ground with an initial velocity of 24 ft/s. Which system of equations can be used to model this situation?
A
The length of a rectangular field is represented by the expression 14x-3x^2 The width of the field is represented by the expression 5x-7x^2+7y. How much greater is the length of the field than the width?
A
The volume of a rectangular prism is (x^3 - 3x^2 + 5x - 3), and the area of its base is (x^2 - 2). If the volume of a rectangular prism is the product of its base area and height, what is the height of the prism?
A
Two boats depart from a port located at (-8, 1) in a coordinate system measured in kilometers and travel in a positive x-direction. The first boat follows a path that can be modeled by a quadratic function with a vertex at (1, 10), whereas the second boat follows a path that can be modeled by a quadratic function with a vertex at (0, -7). Which system of equations can be used to determine whether the paths of the boats cross?
A
What is the additive inverse of the polynomial? -7y^2+x^2y-3xy-7x^2
A
What is the product? (x^4)(3x^3-2)(4x^2+5x)
A
Which expression is equivalent to (2g^5)^3/(4h^2)^3
A
Which expression is equivalent to 9x^5 y^16/ 45x^5 y^4
A
Which is the graph of an even monomial function?
A
Which graph shows rotational symmetry?
A (shape of squiggle line)
Louis used a quadratic equation to model the height, y, of a falling object x seconds after it is dropped. Which ordered pair generated by this model should be discarded because the values are unreasonable?
A. (-4, 1)
What are the roots of the polynomial equation x^4+x^3=4x^2+4x? Use a graphing calculator and a system of equations.
A. -2, -1, 0, 2
What is the quotient (125 - 8x^3) ÷ (25 + 10x + 4x^2)?
A. -2x + 5
Which term, when added to the given polynomial, will change the end behavior of the graph? y = 14x^8 - 6x^5 - 2x^4 - 10
A. -6x^9
Subtract 15mn - 22m +2n from 14mn - 12m +7n.
A. -mn + 10m + 5n
What function is graphed below?
A. -x^2
Which expression is equivalent to 7a^3(6a^2+a)^2 -4a^6
A. 252a^7+80a^6+7a^5
A firework is launched into the air from ground level with an initial velocity of 128 ft/s. If acceleration due to gravity is -16 ft/s^2, what is the maximum height reached by the firework?
A. 256 ft
Which expression is equivalent to x+2+[4x- x^2+6x+8/x+4
A. 4x
How many turning points can a polynomial with a degree of 7 have?
A. 6 turning points
Which statement is true?
A. All constants are of degree 0.
Which statement best describes how to determine whether f(x) = x^4 - x^3 is an even function?
A. Determine whether (-x)^4 - (-x)^3 is equivalent to x^4 - x^3.
Which statement about 6x^2 + 7x - 10 is true?
A. One of the factors is (x + 2).
The graphs of two polynomial equations do not intersect. Kelly concludes that the system has no solution. Which statement best explains why Kelly's reasoning is correct or incorrect?
A. She is incorrect because systems may have only complex solutions which are not visible on a graph.
If X=6 is the only x-intercept of the graph of a quadratic equation, which statement best describes the discriminant of the equation?
A. The discriminant is 0.
A quarterback throws an incomplete pass. The height of the football at time t is modeled by the equation h(t) = -16t2 + 40t + 7. Rounded to the nearest tenth, the solutions to the equation when h(t) = 0 feet are -0.2 s and 2.7 s. Which solution can be eliminated and why?
A. The solution -0.2 s can be eliminated because time cannot be a negative value.
If the discriminant of a quadratic equation is equal to -8, which statement describes the roots?
A. There are two complex roots.
What is the domain of the square root function graphed below?
A. X>-4
The graph of an equation with a negative discriminant always has which characteristic?
A. no x-intercept
A system of three linear equations in three variables is inconsistent. How many solutions to the system exist?
A. none
The formula for the volume of a cube is V(s) = s^3 where s is the side length of the cube. In which quadrant(s) is the graph of the function V(s)?
A. quadrant I
Which law would you use to simplify the expression 3^10/3^4
A. quotient of powers
What is the first step in simplifying the expression 11x-2-3(1-7x)^2 divided (x-1)
A. square the binomial
Which quadratic equation is equivalent to (x2 - 1)^2 - 11(x^2 - 1) + 24 = 0?
A. u^2 - 11u + 24 = 0 where u = (x^2 - 1)
What is the quotient of the following division problem?
A. x + 2
Which expression is a trinomial?
A. x + y - 13
Solve x^2 + 20x + 100 = 36 for x.
A. x = -16 or x = -4
Which expression is equivalent to (x+1)^2-9/x+4
A. x-2
What are the solutions of the equation x^2+4x+4=25
A. x=3 or x= -7
Which equation could generate the curve in the graph below?
A. y = 3x^2 - 2x + 1
Which is an odd monomial function?
A. y=2x^3
Which monomial function has a minimum value?
A. y=5x^10
What are the solutions of the equation x^4 + 3x^2 + 2 = 0? Use u substitution to solve.
B
What is the completely factored form of x^4 + 8x^2 - 9?
B
What is the factored form of x^12 y^18+1
B
What is the sum of the polynomials? (6x+7+x^2)+(2x^2-3)
B
Which equation can be solved by using this system of equations? {y=3x^5-5x^3+2x^2-10x+4 {y=4x^4+6x^3-11
B
Which equation is the inverse of (x-4)^2-2/3=6y-12?
B
Which equation is the inverse of y = x^2 - 36?
B
Which expression is equivalent to (4x^3 y^5)(3x^5 y)^2
B
Which expression is equivalent to 5r^6 t^4 (4r^3 s^2 t^4/ 2r^4 st^6)
B
Solve x^2 - 10x + 25 = 35 for x.
B.
Using the quadratic formula to solve 5x = 6x^2 - 3, what are the values of x?
B.
What are the solutions of the equation x^6 + 6x^3 + 5 = 0? Use factoring to solve.
B.
What is the difference of the polynomials? (x^4+x^3+x^2+x)-(x^4-x^3+x^2-x)
B.
What is the solution of the equation (x - 5)^2 + 3(x - 5) + 9 = 0? Use u substitution and the quadratic formula to solve.
B.
Which equation can be solved by using this system of equations? {y=3x^5-5x^3+2x^2-10x+4 {y=4x^4+6x^3-11
B.
Which expression is equivalent to (2g^3+4)^2
B.
Which expression is equivalent to (4x^3 y^5)(3x^5 y)^2?
B.
Which expression is equivalent to 9x - (x - 8)(x + 1) + 10x?
B.
Which graph shows a polynomial function with a positive leading coefficient?
B.
The financial planner for a beauty products manufacturer develops the system of equations below to determine how many combs must be sold to generate a profit. The linear equation models the income, in dollars, from selling x plastic combs; the quadratic equation models the cost, in dollars, to produce x plastic combs. According to the model, for what price must the combs be sold? {y=x/2 {y=-0.03(x-95)^2+550
B. $0.50 each
What is the factored form of a^2 - 121?
B. (a - 11)(a + 11)
Which graph represents an odd function?
B. (squiggle line)
Which polynomial is in standard form?
B. -16x^2-9x+12
At which root does the graph of f(x) = (x - 5)^3(x + 2)^2 touch the x axis?
B. -2
What are the roots of the polynomial equation x^3-7x=6x-12? Use a graphing calculator and a system of equations.
B. -4, 1, 3
What is the remainder of the following division problem?
B. 1
Which polynomial is in standard form?
B. 12x^5-6x^2-9x+12
A company plans to sell pens for $2 each. The company's financial planner estimates that the cost, y, of manufacturing the pens is a quadratic function with a y-intercept of 120 and a vertex of (250, 370). What is the minimum number of pens the company must sell to make a profit?
B. 174
Which polynomial is in standard form?
B. 18x^5-7x^2y-2xy^2+17y^4
Which equation can be solved using the expression ^ -3+-squareroot/(3)^2+4(10)(2)/ 2(10) for x
B. 2 = 3x + 10x2
The owner of an office building is expanding the length and width of a parking lot by the same amount. The lot currently measures 120 ft by 80 ft, and the expansion will increase its area by 4,400 ft^2. By how many feet should the length of the parking lot be increased?
B. 20 ft
The total area of two square windows is 1,025 in.^2. Each side of the larger window is 5 in. longer than the sides of the smaller window. How long are the sides of the smaller window?
B. 20 in.
Which expression is equivalent to 60^20y^24/30x^10y^12
B. 2x^10y^12
Which value must be added to the expression x^2 + 12x to make it a perfect-square trinomial?
B. 36
Which expression is equivalent to 15a^8 b^4/5a^4 b?
B. 3a^4 b^3
Which equation can be solved by using this system of equations? {y=3x^3-7x^2+5 {y=7x^4+2x
B. 3x^3-7x^2+5=7x^4+2x
Which expression is equivalent to 4 - (2m - 3)?
B. 4 - 2m + 3
What is the sum of the polynomials?
B. 4m - 24n + 3
If f(x)= square root/4x+9+2, which inequality can be used to find the domain of f(x)?
B. 4x+9+2
A cube has side length x. One side of the cube is increased by 4 inches, and another side is doubled. The volume of the new rectangular prism is 450 cubic inches. The equation 2x^3+8x^2=450 can be used to find x. What was the side length of the original cube? Use a graphing calculator and a system of equations to find the answer.
B. 5 inches
A function is a sixth-degree polynomial function. How many turning points can the graph of the function have?
B. 5 or less
How many turning points are in the graph of the polynomial function?
B. 5 turning points
A skydiver jumps from an airplane at an altitude of 2,500 ft. He falls under the force of gravity until he opens his parachute at an altitude of 1,000 ft. Approximately how long does the jumper fall before he opens his chute?
B. 9.7 s
Which value must be added to the expression x^2 - 3x to make it a perfect-square trinomial?
B. 9/4
Carmen is using the quadratic equation (x + 15)(x) = 100 where x represents the width of a picture frame. Which statement about the solutions x = 5 and x = -20 is true?
B. The solution x = 5 should be kept, but x = -20 is unreasonable.
Given that (1, 0, 1) is a solution to a system of three linear equations, which of the following is true about the system?
B. The system can be either independent or dependent.
If the discriminant of a quadratic equation is 4, which statement describes the roots?
B. There are two real roots.
Which values of a and b make the equation true?
B. a = 3, b = 3
What is the cube root of b^27
B. b^9
Let a and b be real numbers where a mc021-1.jpg b mc021-2.jpg 0. Which of the following functions could represent the graph below?
B. f(x) = (x - a)^2(x - b)^4
Which monomial function is described by the following statements? As x > 0 increases, f(x) increases. As x < 0 decreases, f(x) decreases.
B. odd monomial function with positive a
A system of three linear equations in three variables is consistent and independent. How many solutions to the system exist?
B. one
Which expression is equivalent to r^9/r^3
B. r^6
What substitution should be used to rewrite 16(x^3 + 1)^2 - 22(x^3 + 1) - 3 = 0 as a quadratic equation?
B. u = (x^3 + 1)
What are the solutions of the equation (x + 2)^2 - 2(x + 2) - 15 = 0? Use u substitution to solve.
B. x = -5 and x = 3
What are the solutions of the equation x^6 - 9x^3 + 8 = 0? Use u substitution to solve.
B. x = 1 and x = 2
What is the solution to the following system? {4x+3y-z=-6 {6x-y+3z=12 {8x+2y+4z=6
B. x = 1, y = -3, z = 1
What are the solutions of the equation x^4 - 5x^2 - 36 = 0? Use factoring to solve.
B. x = ±2i and x = ±3
If f(x)=squareroot/x-3, which inequality can be used to find the domain of f(x)?
B. x-3>0
What is the quotient (x^3 + 8) ÷ (x + 2)?
B. x2 - 2x + 4
Which monomial function has a maximum value?
B. y=-5x^4
Which function is symmetric with respect to the y axis?
B. y=3x^6
What is the product? (3a^2 b^7)(5a^3 b^8)
C
What is the product? (3x-6)(2x^2-7x+1)
C
What is the product? (7x^2 y^3)(3x^5 y^8)
C
Which equation is the inverse of y = x^2 + 16?
C
Which expression is equivalent to (m^5 n/pq^2)^4
C
Which of the following could be the graph of y = x^n where n is even?
C
Which graph represents an even function?
C (shape of n)
What are the roots of the polynomial equation x^3-5x+5=2x^2-5? Use a graphing calculator and a system of equations. Round noninteger roots to the nearest hundredth.
C. -2.24, 2, 2.24
Sharon is jumping from an 18-foot diving board with an initial upward velocity of 4 ft/s. When Susan jumps, Megan throws a beach ball up to Susan with an initial upward velocity of 16 ft/s from a height 5 feet off the ground. To the nearest hundredth of a second, how long after she jumps does the ball reach Sharon?
C. 1.08 seconds
Which polynomial is in standard form?
C. 11x^3-6x^2+5x
The length of a rectangular field is 20 less than its width. The area of the field is 12,000 ft^2. What is the width of the field?
C. 120 ft
A projectile is launched straight up with an initial velocity of 120 ft/s. If acceleration due to gravity is -16 ft/s^2, after about how many seconds will the object reach a height of 200 ft?
C. 2.5 s
Alice's backyard is a rectangular piece of property that is twice as long as it is wide. The total area of her yard is 1,000 m2. What is the approximate width of her backyard?
C. 22.4 m
A car's stopping distance in feet is modeled by the equation d(v)= 2.15v^2/58.4f where v is the initial velocity of the car in miles per hour and f is a constant related to friction. If the initial velocity of the car is 47 mph and f = 0.34, what is the approximate stopping distance of the car?
C. 239 feet
Dimitri is solving the equation x^2 - 10x = 21. Which value must be added to both sides of the equation to make the left side a perfect-square trinomial?
C. 25
Which expression is a sum of cubes?
C. 27x^9+y^6
Which expression is equivalent to 16^3?
C. 2^12
What is the sum of the polynomials? (m + n + 3) + (m + n + 4)
C. 2m + 2n + 7
Which expression is equivalent to (5x^3)(2x)^3
C. 40x^6
Which expression is equivalent to (3m)(4m)^2?
C. 48m^3
Which expression is equivalent to 5^10 * 5^5
C. 5^5
Which expression is a trinomial of degree 1?
C. 6 + x - y
Which equation is quadratic in form?
C. 7x^6 + 36x^3 + 5 = 0
Which expression is equivalent to (2x^2)(3x^3)(4x)^2?
C. 96^7
Which best describes the end behavior of y=7x^2?
C. As x > 0 increases, f(x) increases. As x < 0 decreases, f(x) increases.
Marcus finds that (3x^2-2y^2+5x)+(4x^2+12y^2-7x)=7x^2-10y^2-2X What error did Marcus make?
C. He combined the terms -2y^2 and 12y^2 incorrectly.
Which statement best describes the polynomial? 6-8y+14y^7+16y^8
C. It is not in standard form because the exponents are not in order from highest to lowest.
Anja divides (8x^3 - 36x^2 + 54x - 27) by (2x - 3) as shown below. What error does Anja make?
C. She makes a multiplication error.
If x = -3 is the only x-intercept of the graph of a quadratic equation, which statement best describes the discriminant of the equation?
C. The discriminant is 0.
Which statement best describes the equation x^5 + x^3 - 14 = 0?
C. The equation is not quadratic in form because it cannot be rewritten as a second-degree polynomial.
Which statement describes the graph of f(x) = 4x^7 + 40x^6 + 100x^5?
C. The graph crosses the x axis at x = 0 and touches the x axis at x = -5.
The first equation in the system models the heights in feet, h, of a falling baseball as a function of time, t. The second equation models the heights in feet, h, of the glove of a player leaping up to catch the ball as a function of time, t. Which statement describes the situation modeled by this system? {h=35-16t {h=6+18t-16t^2
C. The height of the baseball is 35 feet at the moment the player begins to leap.
The center of an ice rink is located at (0, 0) on a coordinate system measured in meters. Susan is skating along a path that can be modeled by the equation y = 6x - x^2 - 5. Luke starts at (10, -21) and skates along a path that can be modeled by a quadratic function with a vertex at (8, -9). If the rink is a circle with a radius of 35 meters, which statement best interprets the solution(s) of a system of equations modeling the paths of the skaters?
C. The skaters path intersect twice, but only one of those points is inside the rink.
Which classification best describes the following system of equations? { 5x+y+2z=13 {4x+3y+6z=17 { x+2y=4
C. consistent and independent
Which classification best describes the following system of equations? {12x+5y-3z=36 { x-2y+4z=3 {9x-10y+5z=27
C. consistent and independent
If a polynomial has four terms, 3x^3 + 5x + 6x^2 + 10, which factoring method can be considered?
C. factor by grouping
What substitution should be used to rewrite 4x^12 - 5x^6 - 14 = 0 as a quadratic equation?
C. u = x^6
Which quadratic equation is equivalent to (x + 2)^2 + 5(x + 2) - 6 = 0?
C. u^2 + 5u - 6 = 0 where u = (x + 2)
The quotient of (x^4 + 5x^3 - 3x - 15) and a polynomial is (x^3 - 3). What is the polynomial?
C. x + 5
Solve x^2 - 14x + 31 = 63 for x.
C. x = -2 or x = 16
What is the solution to the following system? {x+2y+z=9 {x-y+3z=13 { 2z=10
C. x = 0, y = 2, z = 5
Which equation can be simplified to find the inverse of y = x^2 - 7?
C. x = y^2 - 7
What is the completely factored form of x^3 - 64x?
C. x(x - 8)(x + 8)
If x^2 + mx + m is a perfect-square trinomial, which equation must be true?
C. x2 + mx + m = (x + 2)^2
What is the domain of the function y=2squareroot/x-5
C. x>5
The long division below shows the first term of the quotient. Which polynomial should be subtracted from the dividend first?
C. x^3 + 2x^2
A box is to be constructed with a rectangular base and a height of 5 cm. If the rectangular base must have a perimeter of 28 cm, which quadratic equation best models the volume of the box?
C. y = 5(14 - x)(x)
What function is graphed below?
C. y=-6x^5
The president of a company creates a graph of the price of the company's stock over one year. He describes the graph as follows: • The price of the stock rose to about $17 before falling to about $4. • There have only been two periods during which the price of the stock decreased. • The price of the stock is expected to increase in the long run. Which graph correctly shows the price of the stock?
D.
Use completing the square to solve (x - 12)(x + 4) = 9 for x.
D.
Using the quadratic formula to solve x^2 + 20 = 2x, what are the values of x?
D.
What is the end behavior of the graph of the polynomial function y = 7x^12 - 3x^8 - 9x^4?
D.
What is the end behavior of the polynomial function?
D.
Which expression shows the sum of the polynomials with like terms grouped together? (8x+3z-8z^2)+(4y-5z)
D.
Which system of equations can be used to find the roots of the equation 4x^2=x^3+2x
D.
Arlana graphed the system of equations that can be used to solve x^3-5x^2+2=-x^3+17x What are the roots of the polynomial equation? Round noninteger roots to the nearest hundredth.
D. -2, 0.11, 4.39
Arlana graphed the system of equations that can be used to solve x^3-5x^2+2=-x^3+17x What are the roots of the polynomial equation? Round noninteger roots to the nearest hundredth.
D. -2, 0.11, 4.39
What are the roots of the polynomial equation x^3-6x=3x^2-8? Use a graphing calculator and a system of equations.
D. -2, 1, 4
A basketball player is shooting a basketball toward the net. The height, in feet, of the ball t seconds after the shot is modeled by the equation h = 6 + 30t - 16t^2. Two-tenths of a second after the shot is launched, an opposing player leaps up to block the shot. The height of the shot blocker's outstretched hands t seconds after he leaps is modeled by the equation h = 9 + 25t - 16t^2. If the ball reaches the net 1.7 seconds after the shooter launches it, does the leaping player block the shot?
D. No, the shot is not blocked.
Which statement describes the graph of f(x) = -4x^3 - 28x^2 - 32x + 64?
D. The graph touches the x axis at x = -4 and crosses the x axis at x = 1.
What term describes the monomial 14xyz?
D. cubic
Which monomial function, y = ax^n, is described by the following statements? As x > 0 increases, f(x) decreases. As x < 0 decreases, f(x) decreases.
D. even monomial function with negative a
What are the possible degrees for the polynomial function?
D. odd degrees of 5 or greater
What is the correct order of operations for simplifying the expression 2 - 3x + 5 + 7(y - 5x)2 + x?
D. square the binomial, distribute 7 inside the parentheses, and then combine like terms
Which quadratic equation is equivalent to (x - 4)^2 - (x - 4) - 6 = 0?
D. u^2 - u - 6 = 0 where u = (x - 4)
The area of a rectangle is (x^3 - 5x^2 + 3x - 15), and the width of the rectangle is (x^2 + 3). If area = length × width, what is the length of the rectangle?
D. x - 5
What is the solution to the following system? { -4y=8 {x+3y-3z=-26 {2x-5y+5=19
D. x = 1, y = -2, z = 7
What are the solutions of the quadratic equation (x - 8)^2 - 13(x - 8) + 30 = 0? Use u substitution to solve.
D. x = 11 and x = 18
Solve x^2 - 8x + 41 = 0 for x.
D. x = 4 ± 5i
The graph of this system of equations is used to solve 4x^2-3x+6=2x^4-9x^3+2x What represents the solution set?
D. x coordinates of the intersection points
The graph of this system of equations is used to solve 4x^2-3x+6=2x^4-9x^3+2x {y=4x^2-3x+6 {y=2x^4-9x^3+2x
D. x coordinates of the intersection points
What is the factored form of 2x3^ + 4x^2 - x?
D. x(2x^2+4x-1)
The area of a rectangle is (x^3 - 5x^2 + 3x - 15), and the width of the rectangle is (x^2 + 3). If area = length × width, what is the length of the rectangle?
D. x-15
What is the quotient (x^3 - 3x^2 + 5x - 3) ÷ (x - 1)
D. x^2 - 2x + 3
Which equation could generate the curve in the graph below?
D. y = 2x^2 + 8x + 8
Which is an even monomial function?
D. y=-x^10
If f(x) is an odd function, which statement about the graph of f(x) must be true?
a. It has rotational symmetry about the origin.
If f(x) is an even function and (6, 8) is one the points on the graph of f(x), which reason explains why (-6, 8) must also be a point on the graph?
a. Since the function is even, the output of a negative x-value and its opposite is the same.
Which of the following is an even function?
a. f(x) = |x|
The graph of f(x) consists of 14 points. Six of the points lie in Quadrant I of the coordinate plane. If f(x) is an odd function, what is the greatest number of points that can lie in Quadrant II?
a. one
Which graph shows line symmetry about the y-axis?
b
Which expression is equivalent to 9x - (x - 8)(x + 1) + 10x?
b.
Which statement best describes how to determine whether f(x) = x^2 - x + 8 is an even function
b. Determine whether (-x)^2 - (-x) + 8 is equivalent to x^2 - x + 8.
Which statement best compares the graphs of y = -3x^n and y = 3x^n?
b. The graph of y=-3x^n is the reflection of the graph of y=3x^n about the x axis.
Suppose f(x) is a function such that if p < q, f(p) < f(q). Which statement best describes f(x)?
b. f(x) can be odd but cannot be even.
Which of the following is an even function?
b. g(x) = 2x^2 + 1
What are the solutions of the equation (x + 2)^2 - 2(x + 2) - 15 = 0? Use u substitution to solve.
b. x = -5 and x = 3
Which graph represents an odd function?
c
Which statement best describes how to determine whether f(x) = 9 - 4x^2 is an odd function?
c. Determine whether 9 - 4(-x)^2 is equivalent to -(9 - 4x^2).
If f(x) is an even function, which statement about the graph of f(x) must be true?
c. It has line symmetry about the y-axis.
Lucia finds that (3x^2+3x+5)+(7x^2-9x+8)=10x^2-12x+13. What error did Lucia make
c. She combined the terms 3x and -9x incorrectly.
If g(x) is an odd function, which function must be an even function?
c.f(x) = g(x)^2
Which of the following is an odd function?
d. g(x) = 4x
Which of the following is an odd function?
f(x) = 6x^3 + 2x
What is the quotient of (x^3+3x^2-4x-12)divided(x^2+5x+6)
x-2
Which expression is a polynomial?
-13
For which value of m does the graph of y = 18x^2 + mx + 2 have exactly one x-intercept?
12
Which value of a would make the following expression completely factored?
12
A rectangular pan has a length that is 4/3 the width. The total area of the pan is 432 in.^2. What is the width of the cake pan?
18
What value of g makes the equation true? (x-3)(x+5)=x^2+gx-15
2
Given that the values in the table represent the graph of a continuous function, y has at least how many zeros?
5
What is the discriminant of 3x^2 + 6x = 2?
60
What is the degree of 4a^5b^2+2ab^3
7
What is the discriminant of 3x^2-10x=-2
76
Samuel found the difference of the polynomials. (15x^2+11y^2+8x)-(7x^2+5y^2+2x)=___x^2+6y^2+6x What value is missing from his solution
8
A company plans to sell a new type of vacuum cleaner for $280 each. The company's financial planner estimates that the cost, y, of manufacturing the vacuum cleaners is a quadratic function with a y-intercept of 11,000 and a vertex of (500, 24,000). Which system of equations can be used to determine how many vacuums must be sold for the company to make a profit?
A
A coordinate grid is mapped on a video game screen, with the origin in the lower-left corner. A game designer programs a helicopter to follow a path that can be modeled by a quadratic function with a vertex at (16, 20) and passing through the point (4, 25). She also programs an airplane to move along a linear path that passes through the points (0, 18) and (30, 20). Which system of equations can be used to determine whether the paths of the helicopter and airplane cross?
A
Solve x^2 - 12x + 36 = 90 for x.
A.
What are the solutions of the equation (x + 2)^2 + 12(x + 2) - 14 = 0? Use u substitution and the quadratic formula to solve.
A.
Which function has the domain x>-11
A.
Which graph shows a polynomial function of an even degree?
A.
Which graph shows a polynomial function with a negative leading coefficient?
A.
Which of the following could be the graph of y = -x^n where n is odd?
A.
Which expression is a sum of cubes?
A. -27a^3 b^6+8a^9 b^12
Which values of a and b make the following equation true? (5x^7 y^2)(-4x^4 y^5)=-20x^a y^b
A. a = 11, b = 7
Which could be the function graphed below?
A. f(x)= sqaureroot/x-2
A soccer ball is kicked into the air from the ground. If the ball reaches a maximum height of 25 ft and spends a total of 2.5 s in the air, which equation models the height of the ball correctly? Assume that acceleration due to gravity is -16 ft/s^2.
A. h = -16(t - 1.25)^2 + 25
Which statement about the following equation is true? 3x^2 - 8x + 5 = 5x^2
B. The discriminant is greater than 0, so there are two real roots.
Which statement describes how the graph of the given polynomial would change if the term 2x5 is added? y = 8x4 - 2x3 + 5
B. The ends of the graph will extend in opposite directions.
A student factors 3x^2 - 12 to the following. 3(x^2-4) Which statement about 3(x^2 - 4) is true
B. The expression is equivalent, but it is not completely factored.
Which of the following describes the polynomial function?
B. The function has an odd degree.
Which statement best compares the graphs of y = -3x^n and y = 3x^n?
B. The graph of y=-3x^n is the reflection of the graph of y=3x^n about the x axis.
A party-favor bag must have a volume of 140 cubic inches and the dimensions that are shown below. The equation x^3+6x^2-27x=140 can be used to find x What are the dimensions of the party-favor bag? Use a graphing calculator and a system of equations to find the answer.
B. The length is 5 inches, the width is 2 inches, and the height is 14 inches.
Which function is symmetric with respect to the origin?
B. y=x^9
Which expression is a perfect cube?
B. y^24
The polynomial equation x^6-16x^2=4x^4-64 has complex roots ±2i. What are the other roots? Use a graphing calculator and a system of equations.
B.-2, 2
A cube with side length 4p is stacked on another cube with side length 2q^2. What is the total volume of the cubes in factored form?
C
A store owner buys $4,000 worth of products. For shipping costs, it is 10% of the amount of product A and 4% of the amount of product B. If the total shipping cost is $352, which system of equations can be used to determine how much of product A and product B the store owner bought?
C
For what values of m does the graph of y = 3x^2 + 7x + m have two x-intercepts?
C
The volume of a rectangular prism is given by the formula V = lwh, where l is the length of the prism, w is the width, and h is the height. Which expression represents the volume of the following rectangular prism?
C
Using the quadratic formula to solve 4x^2 - 3x + 9 = 2x + 1, what are the values of x?
C
What is the completely factored form of 3x^5 - 7x^4 + 6x^2 - 14x?
C
What is the domain of the function Y=squareroot/x+4
C
What is the factored form of x^3-1
C
Dylan uses the expressions (x^2 - 2x + 8) and (2x^2 + 5x - 7) to represent the length and width of his bedroom. Which expression represents the area (lw) of Dylan's room?
C.
If f(x) squareroot/ 1/2x-10+3, which inequality can be used to find the domain of f(x)?
C.
What are the solutions of the equation x^4 + 95x^2 - 500 = 0? Use factoring to solve.
C.
What is the end behavior of the graph of the polynomial function y = 10x^9 - 4x?
C.
What is the end behavior of the polynomial function?
C.
What is the product? (7x^2)(2x^3+5)(x^2-4x-9)
C.
Which graph shows a polynomial function of an odd degree?
C.
The cost for three packages of moving boxes is modeled by the system of equations below. Let s represent small boxes, m represent medium boxes, and l represent large boxes. Which ordered pair (s, m, l) represents the costs of the three boxes? {7s+4m+2/=24 {5s+3m+6/=30 {3s+7m+10/=46
C. (1.50, 2.00, 2.75)
What is the solution to the following system? {3x+3y+6z=9 {x+3y+2z=5 {3x+12y+12z=18
C. (2, 1, 0)
What are the roots of the polynomial equation x^4+x^2=4x^3-12x+12? Use a graphing calculator and a system of equations. Round noninteger roots to the nearest hundredth.
C. -1.73, 1.73
Sandra graphed the system of equations that can be used to solve x^3-2x^2-11x+12=x^3-13x-12
C. -3, 4
Which expression is equivalent to (-7m^4+15m^3-12m^2)+3m^5-12m^4-7m^3)/m-6
C. 3m^4-m^3-2m^2
Which polynomial is factored completely?
C. 3x(9x^2+1)
What is the quotient (3x^4 - 4x^2 + 8x - 1) ÷ (x - 2)?
C. 3x3 + 6x2 + 8x + 24 + 47/x-2
How many turning points are in the graph of the polynomial function?
C. 4 turning points
Solve X^2+11x+121/4=125/4 for x
D
The president of a company creates a graph of the price of the company's stock over one year. He describes the graph as follows: • The price of the stock rose to about $17 before falling to about $4. • There have only been two periods during which the price of the stock decreased. • The price of the stock is expected to increase in the long run. Which graph correctly shows the price of the stock?
D
The volume of a rectangular prism is given by the formula V = lwh, where l is the length of the prism, w is the width, and h is the height. Suppose a box in the shape of a rectangular prism has length (2a + 11), width (5a - 12), and height (a + 6). Which expression represents the volume of the box?
D
What are the solutions of the equation x^4 - 5x^2 - 14 = 0? Use factoring to solve.
D
What is the product? (3a^2 b^4)(-8ab^3)
D
What is the product? (4s+2)(5s^2+10s+3)
D
What is the product? (Y^2+3y+7)(8y^2+y+1)
D
Which equation shows the quadratic formula used correctly to solve 7x^2 = 9 + x for x?
D
Which expression can be used to find the sum of the polynomials? (9-3x^2)+(-8x^2+4x+5)
D
Solve 2x^2 - 5x + 1 = 3 for x.
D.
Which graph represents an even function?
D.
A rectangular prism with a volume of 400 cubic centimeters has the dimensions x + 1 centimeters, 2x centimeters, and x + 6 centimeters. The equation 2x^3+14x^2+12x=400 can be used to find x. What is the length of the longest side? Use a graphing calculator and a system of equations to find the answer.
D. 10 centimeters
Which expression is a possible leading term for the polynomial function graphed below?
D. 22x^9
Which polynomial is in standard form?
D. 23x^9-12x^4+19
What is the remainder when (3x^3 - 2x^2 + 4x - 3) is divided by (x^2 + 3x + 3)?
D. 28x + 30
What is the quotient (2x^4 - 3x^3 - 3x^2 + 7x - 3) ÷ (x2 - 2x + 1)?
D. 2x^2 + x - 3
Which number is a perfect cube?
D. 343
What is the cube root of 27a^12
D. 3a^4
Which equation has the solutions x= 5+2squareroot7/3
D. 3x^2 - 10x - 1 = 0
Which expression is equivalent to 9x^5+3x(4x^4-3x^2)^2
D. 48^9-72x^7+36x^5
Which expression is a difference of cubes?
D. 64c^15-d^27
Which expression is equivalent to (2x^4y)^3
D. 8x^12y^3
What is the sum of the polynomials? (9x^2-12y^2-11x)+(x^2-3y^2-7x)
D. 9x^2-12y^2-11x
Which statement about 4x^2 + 19x - 5 is true?
D. One of the factors is (x + 5).
What is the domain of the square root function graphed below?
D. X>3
A polynomial function has a root of -7 with multiplicity 2, a root of -1 with multiplicity 1, a root of 2 with multiplicity 4, and a root of 4 with multiplicity 1. If the function has a positive leading coefficient and is of even degree, which statement about the graph is true?
The graph of the function is positive on (-oo, -7).
What function is graphed below?
y=5x^5
