Rate of Change, Algebra II

What is the vertex of the graph of y = x2 + 4x? (-2, -12) (-2, -8) (-2, -6) (-2, -4)

(-2, -4)

If h(x) = x - 7 and g(x) = x2, which expression is equivalent to (g*h)(5)? (5 - 7)2 (5)2 - 7 (5)2(5 - 7) (5 - 7)x2

(5 - 7)^2

The axis of symmetry of a quadratic equation is x = -3. If one of the zeroes of the equation is 4, what is the other zero? -10 -7 -6 -4

-10

Given h(f)=-2(t+5)^2+4, find h(-8) -334 -14 45 445

-14

Which complex number has an absolute value of 5? -3 + 4i 2 + 3i 7 - 2i 9 + 4i

-3 + 4i

What is the range of the function graphed below?

-3<y≤3

Given f(x)=10-2x find f(7). -4 3 7 56

-4

What is the first step when rewriting y = -4x2 + 2x - 7 in the form y = a(x - h)2 + k? 2 must be factored from 2x - 7 -4 must be factored from -4x2 + 2x x must be factored from -4x2 + 2x -4 must be factored from -4x2 - 7

-4 must be factored from -4x2 + 2x

if i=sqr-1 what is the value of i3

-i

Greg is in a car at the top of a roller-coaster ride. The distance, d, of the car from the ground as the car descends is determined by the equation d = 144 - 16t2, where t is the number of seconds it takes the car to travel down to each point on the ride. For which interval of time is Greg's car moving in the air?

0<t<3

An acorn falls from the branch of a tree to the ground 25 feet below. The distance, S, that the acorn is from the ground as it falls is represented by the equation S(t) = -16t2 + 25, where t is the number of seconds. For which interval of time is the acorn moving through the air?

0<t≤5/4

Which phrase best describes the translation from the graph y = 6x2 to the graph of y = 6(x + 1)2? 6 unit left 6 unit right 1 unit left 1 unit right

1 unit left

If h(x) = 5 + x and k(x)=1/x, which expression is equivalent to (k*h)(x)?

1/(5+x)

The path of a football kicked by a field goal kicker can be modeled by the equation y = -0.04x2 + 1.56x, where x is the horizontal distance in yards and y is the corresponding height in yards. What is the approximate maximum height of the football? 15.21 yd 19.5 yd 38.94 yd 45.63 yd

15.21 yd

Which of the following is equivalent to 18-sqr-25

18-5i

If the complex number x = 3 + bi and |x|2 = 13, which is a possible value of b?

2

If f(x) = x3 - 2x2, which expression is equivalent to f(i)? -2 + i -2 - i 2 + i 2 - i

2 - i

The profit a company makes from producing x tabletops is modeled by the equation P(x) = 480x - 2x2. For what number of tabletops does the company make a profit of $0? 100 tabletops 120 tabletops 240 tabletops 480 tabletops

240 tabletops

What is the discriminant of 9x2 + 2 = 10x? -356 -172 28 72

28

Which complex number is represented by the point graphed on the complex plane below?

3 - 4i

What is the first step when rewriting y = 3x2 + 9x - 18 in the form y = a(x - h)2 + k? 3 must be factored from 3x2 + 9x x must be factored from 3x2 + 9x 9 must be factored from 9x - 18 3 must be factored from 3x2 - 18

3 must be factored from 3x2 + 9x

The square of a number is 12 less than 7 times the number. What is the number? -4 or -3 -4 or 3 -3 or 4 3 or 4

3 or 4

If f(x) = x2 + 1 and g(x) = x - 4, which value is equivalent to (f*g)(10)? 37 97 126 606

37

Equation

3x2 - 10x - 1 = 0

Which complex number has a distance of sqr17 from the origin on the complex plane?

4 - i

A rectangular deck is 12 ft by 14 ft. When the length and width are increased by the same amount, the area becomes 288 sq. ft. By how much were the dimensions increased? 2 ft 4 ft 8 ft 10 ft

4 ft

Which phrase best describes the translation from the graph y = 2(x - 15)2 + 3 to the graph of y = 2(x - 11)2 + 3? 4 units to the left 4 units to the right 8 units to the left 8 units to the right

4 units to the left

If s(x) = x - 7 and t(x) = 4x2 - x + 3, which expression is equivalent to (t*s)(x)? 4(x - 7)2 - x - 7 + 3 4(x - 7)2 - (x - 7) + 3 (4x2 - x + 3) - 7 (4x2 - x + 3)(x - 7)

4(x - 7)^2 - (x - 7) + 3

Given b(x)=|x+4|, what is b(-10)?

6

What is the first step when rewriting y = 6x2 + 18x + 14 in the form y = a(x - h)2 + k? 16 must be factored from 18x + 14 x must be factored from 6x2 + 18x 6 must be factored from 6x2 + 14 6 must be factored from 6x2 + 18x

6 must be factored from 6x2 + 18x

What is the discriminant of 3x2 + 6x = 2? 12 18 42 60

60

The cost, C, to produce b baseball bats per day is modeled by the function C(b) = 0.06b2 - 7.2b + 390. What number of bats should be produced to keep costs at a minimum? 27 bats 60 bats 174 bats 390 bats

60 bats

The square of 9 less than a number is 3 less than the number. What is the number? -12 or 7 -12 or -7 -7 or 12 7 or 12

7 or 12

What is the discriminant of 3x^2-10x=-2?

76

If g(x)=x+1/x-2 and h(x) = 4 - x, what is the value of (g*h)(-3)?

8/5

Which equation can be simplified to find the inverse of y = 5x2 + 10?

A

Which equation is the inverse of y = 100 - x2?

A

Which equation is the inverse of y = 2x2 - 8?

A

Which equation shows the quadratic formula used correctly to solve 5x2 + 3x - 4 = 0 for x?

A

Which graph shows a function whose inverse is also a function?

A.

In which function is x = 2 mapped to 32?

B

Using the quadratic formula to solve 7x2 - x = 7, what are the values of x?

B

What is the domain of the function y=sqr x+6-7

B

Which table represents the same relation as the set {(-6,4),(-4,0).(-3,2).(-1,2)}

B

if f(x)=sqr x-3, which inequality can be used to find the domain of f(x)?

B

If f(x) and g(x) are inverse functions of each other, which of the following shows the graph of f(g(x))?

B.

Which function is the inverse of f(x) = 2x + 3?

B.

If f(x) and f-1(x) are inverse functions of each other and f(x)=2x+5 what is f-1(8)?

B. 3/2

Which statement could be used to explain why f(x) = 2x - 3 has an inverse relation that is a function? The graph of f(x) passes the vertical line test. f(x) is a one-to-one function. The graph of the inverse of f(x) passes the horizontal line test. f(x) is not a function.

B. f(x) is a one-to-one function.

The formula for the volume of a sphere is V=3/4πr^3 What is the formula solved for r?

C

What is the domain of the function y=sqr x+4

C

Which equation can be simplified to find the inverse of y = x2 - 7?

C

Which graph represents the same relation as the rule y = 2x, for all real numbers x?

C

If f(x) = 5x, what is f-1(x)?

C.

If f(x)=5x-25 and g(x)=1/5x+5

C.

If f(x) = 3x and g(x)=1/3x which expression could be used to verify that g(x) is the inverse of f(x)?

C. 1/3(3x)

Which function has an inverse that is also a function? {(-1, -2), (0, 4), (1, 3), (5, 14), (7, 4)} {(-1, 2), (0, 4), (1, 5), (5, 4), (7, 2)} {(-1, 3), (0, 4), (1, 14), (5, 6), (7, 2)} {(-1, 4), (0, 4), (1, 2), (5, 3), (7, 1)}

C. {(-1, 3), (0, 4), (1, 14), (5, 6), (7, 2)}

The domain of f(x) is the set of all real values except 7, and the domain of g(x) is the set of all real values except -3. Which of the following describes the domain of (G*f)(x)

D

What is the domain of the square root function graphed below?

D

Which equation can be simplified to find the inverse of y = 2x2?

D

Which equation is the inverse of 2(x - 2)2 = 8(7 + y)?

D

Which equation is the inverse of 5y+4=(x+362+1/2

D

Which equation is the inverse of y = 16x2 + 1?

D

Which graph represents the same relation as the table below?

D

Which relation below represents a one-to-one function?

D

In which quadrant is the number -14 - 5i located on the complex plane? I II III IV

III

The function C(x) = 400x - 0.2x2 represents the total costs for a company to produce a product, where C is the total cost in dollars and x is the number of units sold. Which statement is true? One thousand units have the minimum cost of $200,000. One thousand units have the maximum cost of $200,000. Two thousand units have the minimum cost of $800,000. Two thousand units have the maximum cost of $800,000.

One thousand units have the maximum cost of $200,000.

If x = -3 is the only x-intercept of the graph of a quadratic equation, which statement best describes the discriminant of the equation?

The discriminant is 0.

If x=6 is the only x-intercept of the graph of a quadratic equation, which statement best describes the discriminant of the equation?

The discriminant is 0.

Which statement could be used to explain why the function h(x) = x3 has an inverse relation that is also a function? The graph of h(x) passes the vertical line test. The graph of the inverse of h(x) is a vertical line. The graph of the inverse of h(x) passes the horizontal line test. The graph of h(x) passes the horizontal line test.

The graph of h(x) passes the horizontal line test.

If the domain of the square root function f(x) is mc024-1.jpg, which statement must be true? 7 is subtracted from the x-term inside the radical. The radical is multiplied by a negative number. 7 is added to the radical term. The x-term inside the radical has a negative coefficient.

The x-term inside the radical has a negative coefficient.

If the discriminant of a quadratic equation is equal to mc027-1.jpg, which statement describes the roots? There are two complex roots. There are two real roots. There is one real root. There is one complex root.

There are two complex roots.

The graph shows the distance a ball has traveled x seconds after it was thrown. What is the average speed between 2 seconds and 8 seconds.

a. 0.5 meters per second

(d) is a function that relates the number of tickets sold for a movie to the number of days since the movie was released. The average rate of change in T(d) for the interval d = 4 and d = 10 is 0. Which statement must be true?

a. The same number of tickets was sold on the fourth day and tenth day.

If y varies directly as x, and y is 48 when x is 6, which expression can be used to find the value of y when x is 2?

a. y = 48/6 (2)

The cost of soup, s, varies directly with the number of cans, c. When c is 4, the cost is $3. Which graph represents the cost of the soup?

c.

If y varies directly as x, and y is 180 when x is n and y is n when x is 5, what is the value of n?

c. 30

Maria created a graph of B(t), the temperature over time. For the interval between t = 3 and t = 7, the average rate of change in her graph of B(t) is 8. Which statement must be true?

c. The temperature was 32 degrees higher when t = 7 than when t = 3.

Which expression can be used to determine the average rate of change in f(x) over the interval [2, 9]?

d. f(9) - f(2) / 9-2

The height, h, of a falling object t seconds after it is dropped from a platform 300 feet above the ground is modeled by the function h(t)= 300 - 16t^2. Which expression could be used to determine the average rate at which the object falls during the first 3 seconds of its fall?

d. h(3) - h(0) / 3

Which relation is a direct variation that contains the ordered pair (2, 7)?

d. y= 7/2x

If g(x)=2x and (f*g)(x)=3/x, what is f(x)

f(x)=6/x

Which could be the function graphed below?

f(x)=sqr x -2

The average rate of change of g(x) between x = 4 and x = 7 is 5/6. Which statement must be true?

g(7) - g(4) / 7-4 = 5/6

Which function is a quadratic function? h(t) = 12 - 8t + 6t3 g(t) = 7t2 + 3t3 + 2t k(t) = 3t4 + 3t2 + 4 h(t) = 12 - t + 6t2

h(t) = 12 - t + 6t2

If m(x)=x+5/x-1 and n(x)=x-3, which function has the same domain as (m*n)(x)

h(x)=11/x-4

What is the square root of -1? -i i -1 1

i

The solutions to a quadratic equation are x = 2 and x = 7. If k is a nonzero constant, which of the following must be equal to the quadratic equation?

k(x-2)(x-7)=0

Reyna runs a textile company that manufactures T-shirts. The profit, p, made by the company is modeled by the function p=s2+9s-142, where s is the number of T-shirts sold. How many T-shirts should be sold to earn a profit of more than $2,000?

s > 42

What is the solution set of the quadratic inequality 6x^2+1≤0?

slashed out 0

If f(x) = 1 - x, which value is equivalent to |f(i)|?

sqr2

The height of a baseball hit from a bat is modeled by a quadratic function of time, h(t). What does the second coordinate of the vertex of the quadratic function represent? the minimum height of the baseball the time at which the baseball hits the ground the time at which the baseball hits the maximum height the maximum height of the baseball

the maximum height of the baseball

A rectangular patio is 9 ft by 6 ft. When the length and width are increased by the same amount, the area becomes 88 sq ft. Ginger is using the zero product property to solve the equation (6 + x)(9 + x) = 88. What do her solutions represent? one possible length and one possible width two possible amounts for the widths two possible amounts for the lengths two possible amounts by which the dimensions were increased

two possible amounts by which the dimensions were increased

Lisa is using the equation x2 + (x - 5)2 = 157 to find two numbers that differ by 5 and that have squares that sum to 157. When Lisa solves the problem using the zero product property, what do the two solutions represent? two numbers that differ by 5 and squares that have a sum of 157 one possible number is 5 less than the other number one possible number that can be used to find numbers that differ by 5 and squares that have a sum of 157 two possible numbers that can be used to find numbers that differ by 5 and squares that have a sum of 157

two possible numbers that can be used to find numbers that differ by 5 and squares that have a sum of 157

What is the vertex and the equation of the axis of symmetry of the graph of Y=x^2-6x-7? vertex: (-16, 3) a.o.s: x = -16 vertex: (-3, 20) a.o.s: x = -3 vertex: (3,-16) a.o.s: x = 3 vertex: (20, -3) a.o.s: x = 20

vertex: (3,-16) a.o.s: x = 3

What is the axis of symmetry for the graph of y - 4x = 7 - x2 ? x = 2 y = 2 x = 11 y = 11

x = 2

What are the solutions to the equation 3(x - 4)(x + 5) = 0? x = -4 or x = 5 x = 3, x = 4, or x = -5 x = 3, x = -4, or x = 5 x = 4 or x = -5

x = 4 or x = -5

What are the solutions to the equation (x - 6)(x + 8) = 0? x = -6 or x = 8 x = -6 or x = -8 x = 6 or x = -8 x = 6 or x = 8

x = 6 or x = -8

The graph below represents the solution set of which inequality? -4 to 2

x2 + 2x - 8 < 0

equation

x2 - 2x - 4 = 0

What is the equation of the axis of symmetry of the graph of y=ax^2+bx+c

x=-b/2a

The solutions to the equation 2x^2+x-1=2 are x=-3/2 or

x=1

Which equation has a graph that is a parabola with a vertex at (-1, -1)? y = (x - 1)2 + 1 y = (x - 1)2 - 1 y = (x + 1)2 + 1 y = (x + 1)2 - 1

y = (x + 1)2 - 1

Which equation has a graph that is a parabola with a vertex at (-2, 0)? y = -2x2 y = (x + 2)2 y = (x - 2)2 y = x2 - 2

y = (x + 2)2

Which equation has a graph that is a parabola with a vertex at (5, 3)? y = (x - 5)2 + 3 y = (x + 5)2 + 3 y = (x - 3)2 + 5 y = (x + 3)2 + 5

y = (x - 5)2 + 3

Which pair of equations generates graphs with the same vertex? y = -(x + 4)2 and y = (x - 4)2 y = -4x2 and y = 4x2 y = -x2 - 4 and y = x2 + 4 y = (x - 4)2 and y = x2 + 4

y = -4x2 and y = 4x2

Which equation is y = 6x2 + 12x - 10 rewritten in vertex form? y = 6(x + 1)2 - 11 y = 6(x + 1)2 - 10 y = 6(x + 1)2 - 4 y = 6(x + 1)2 - 16

y = 6(x + 1)2 - 16

If (z*z)(x)=1/16x, what is z(x)

z(x)=x/4

Which graph represents the same relation as the set

{(-3,2).(5,5).(3,3).(3-2)}

What are the solutions to the inequality (x-3)(x+5)≤0

{x|-5≤x≤3}

What is the solution set of the quadratic inequality 4(x + 2)2≤0

{x|x=-2}

What is the solution set of the quadratic inequality f(x)≥0?

{x|xER}

If f(x)=x-3/x and g(x)=5x-4, what is the domain of (f*g)(x)?

{x|x≠4/5}

What is the solution set to the inequality (4x-3)(2x-1)≥0?

{x|x≤1/2 or x≥3/4}