Algebra 1
Which equation shows an example of the associative property of addition? (-4 + i) + 4i = -4 + (i + 4i) (-4 + i) + 4i = 4i + (-4i + i) 4i × (-4i + i) = (4i - 4i) + (4i × i) (-4i + i) + 0 = (-4i + i)
(-4 + i) + 4i = -4 + (i + 4i)
(1) As |a| increases, the parabola becomes ___ (2) As |a| decreases, the parabola becomes ___
(1) narrower (2) wider
Which subtraction expressionhas the difference 1 + 4i? (-2 + 6i) - (1 - 2i) (-2 + 6i) - (-1 - 2i) (3 + 5i) - (2 - i) (3 + 5i) - (2 + i)
(3 + 5i) - (2 + i)
Which pair of complex factors results in a real-number product? 15(-15i) 3i(1-3i) (8 + 20i)(-8 - 20i) (4+7i)(4-7i)
(4+7i)(4-7i)
Which addition expressionhas the sum 8 - 3i ? (9 + 2i) + (1 - i) (9 + 4i) + (-1 - 7i) (7 + 2i) + (1 - i) (7 + 4i) + (-1 - 7i)
(9 + 4i) + (-1 - 7i)
Which equation illustrates the identity property of multiplication? (a + bi) × c = (ac + bci) (a + bi) × 0 = 0 (a + bi) × (c + di) = (c + di) × (a + bi) (a + bi) × 1 = (a + bi)
(a + bi) × 1 = (a + bi)
Subtract (3 + 2i) from (-9 - 8i). -17 - 5i -6 - 6i -12 - 10i 12 + 10i
-12 - 10i
Select the correct answer from the choices given(13 + 4i) + n = 0What is n? 0 1 -13 + 4i -13 - 4i
-13 - 4i
What is the first step when rewriting y = -4x² + 2x - 7 in the form y = a(x - h)² + k?
-4 must be factored from -4x² + 2x
If , i= squareroot -1 what is the value of i^3? -1 i 1 -i
-i
Complete the expression so it forms a perfect-square trinomial. x² - 5x + 5/25/4✔ 25/4 x² + ✔ 1477/2 x + 49
.
Simplify each expression. Select the correct answer from the drop-down menu. −6(3i)(−2i) = ✔ -36 2(3 − i)(−2 + 4i) = ✔ -4 + 28i
.
The solution to x2 - 10x = 24 is ✔ 12 or -2. The solution to 2x2 - 11 = 87 is ✔ 7 or -7 The solution to 3x2 - 12x + 24 = 0 is ✔ 2 + 2i or 2 - 2i
.
Think about plotting points in the complex plane to represent the following numbers: -3+8i 4i 6 5-2i Where is each point located on the graph? -3 + 8i is on the horizontal axison the vertical axisin quadrant I✔ in quadrant II. 4i is on the horizontal axis✔ on the vertical axisin quadrant Iin quadrant IV. 6 is ✔ on the horizontal axison the vertical axisin quadrant Iin quadrant IV. 5 - 2i is on the horizontal axison the vertical axisin quadrant III✔ in quadrant IV.
.
What is the domain of the function y=√x +4?
0<_ x < infinite
(9 - 6i) × m = 9 - 6iWhat is m? 0 1 9 + 6i -9 + 6i
1
Using the quadratic formula to solve x2 + 20 = 2x, what are the values of x?
1 +/- (sq.rt.) 19i
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
Which phrase best describes the translation from the graph y = 6x² to the graph of y = 6(x + 1)²?
1 unit left
The vertex of the graph of y = (x - 1)2 - 5 is (, ).
1, -5 / -3, 2
Complete the statements below that show y = x2 + 2x - 1 being converted to vertex form. Form a perfect-square trinomial.y = x2 + 2x + − 1− Factor the perfect-square trinomial in y = (x2 + 2x + 1) − 1− 1.y = (x + )2 − 1 −1 Simplify.y = (x + 1)2 −
1, 1 / 1 / 2
Write the equation of the function whose graph is shown. y = (x + )2 +
1, 5, 3
(1) If the parabola of the form y = a(x - h)2 + k is always shifted horizontally h units and vertically k units, then its vertex is always (2) Enter the coordinates of the vertex of the graph of y = 2(x + 5)^2 − 4. Vertex: ?
1. (h, k) 2. (-5, -4)
(1) Complete the square to write y = 3x^2 + 12x + 7 in vertex form, y = a(x - h)2 + k. y = 3(x^2 + 4x) + 7 y = 3(x^2 + 4x +4) + 7 - __(a)__ (2) When the above expression is written in vertex form, a is __(b)__, h is __(c)__, and k is __(d)__.
1. a = 12 2. b = 3 , h = -2 , k = -5
Let x = a + bi and y = c + di and z = f + giWhich statements are true? Check all of the boxes that apply. x + y = y + x (x × y) × z = x × (y × z) x - y = y - x (x + y) + z = x + (y + z) (x - y) - z = x - (y - z)
1. x + y = y + x 2. (x × y) × z = x × (y × z) 4. (x + y) + z = x + (y + z)
(1) Choose the equation that shows a step in the process of completing the square on the given quadratic. y = x^2 + 8x - 3 (2) The vertex form of the function is y= (x + __(a)__ )^2 + __(b)__
1. y = x^2 + 8x + 16 - 3 - 16 2. (a) = 4, (b) = -19
If f (x) = √1/2x -10+3, which inequality can be used to find the domain of f(x)?
1/2x-10>_0
Multiply and simplify the product.2i(4 - 5i)Select the product. -2i 2i -10 + 8i 10 + 8i
10 + 8i
What is the value of the product (3 - 2i)(3 + 2i)? 5 9 + 4i 9 - 4i 13
13
Multiply and simplify the product.(3 - 5i)(-2 + 4i)Select the product. 14+ 2i 14 + 22i 15 + 22i 26+2i
14 + 22i
Which equation can be solved using the expression for x? 10x^2 = 3x + 2 2 = 3x + 10x^2 3x = 10x^2 - 2 10x^2 + 2 = -3x
2 = 3x + 10x^2
Which phrase best describes the translation from the graph y = (x + 2)2 to the graph of y = x2 + 3? 2 units left and 3 units up 2 units left and 3 units down 2 units right and 3 units up 2 units right and 3 units down
2 units right and 3 units up
Which phrase best describes the translation from the graph y = (x + 2)² to the graph of y = x² + 3?
2 units right and 3 units up
What is the discriminant of 9x2 + 2 = 10x?
28
Evaluate (2-5i)(p+q)(i) when p=2 and q=5i 29i 29i-20 -21i 29
29i
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
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
Express the following in simplest a + bi form. squareroot 9 + squareroot -39 -9i 3-6i 3+6i 9i
3+6i
Enter the values of h and k so that y = x2 + 6x + 10 is in vertex form. y = (x + )2 +
3, 1
Multiply and simplify the product.-12i × 3iSelect the product. 36 -36 36i -36i
36
Multiply and simplify the product.(8 - 5i)2Select the product. 39 89 39-80i 89-80i
39-80i
Which of the following is an example of a complex number that is not in the set of real numbers? -7 2 + squareroot 3 4 + 9i pie
4 + 9i
Which complex number has a distance of squareroot of 17 from the origin on the complex plane? 2 + 15i 17 + i 20 - 3i 4 - i
4 - i
What is the sum of squareroot of -2 and squareroot of-18 4 squareroot 2 4 squareroot 2i 5 squareroot 2 5 squareroot 2i
4 squareroot 2i
Complete the statements below that show y = 8x2 + 32x + 17 being converted to vertex form. Factor out the leading coefficient. y = 8(x2 + 4x) + 17 Form a perfect-square trinomial. y = 8(x2 + 4x + ) + 17 +
4, -32 / 2, -15
Multiply each pair of factors. Type the product in the space provided. (6 + 3i)(6 − 3i) = (4 − 5i)(4 + 5i) = (−3 + 8i)(−3 − 8i) =
45 41 73
What is the square root of -16? -8i -4i 4i 8i
4i
Which of the following expressions are perfect-square trinomials? Check all of the boxes that apply. x2 - 16x - 64 4x2 +12x + 9 x2 + 20x + 100 x2 + 4x + 16
4x2 +12x + 9 x2 + 20x + 100
Select the expression that is equivalent to . | 4-3 | 1 squareroot 7 5i 5
5
The relationship between voltage, E, current, I, and resistance, Z, is given by the equation E = IZ. If a circuit has a current I = 3 + 2i and a resistance Z = 2 - i, what is the voltage of the circuit? 4 - i 4 + i 8 + i 8 + 7i
8 + i
What is the additive inverse of the complex number -8 + 3i? -8 - 3i -8 + 3i 8 - 3i 8 + 3i
8 - 3i
Which equation is y = 6x2 + 12x - 10 rewritten in vertex form?
D. y = 6(x + 1)2 - 16
In which quadrant is the number -14 - 5i located on the complex plane? I II III IV
III
Which equation can be solved using the expression for x?-3+*3^2+10.2/2.10
NOT A
Which equation has the solutions x=-3+*3i/2
NOT A
Which equation has the solutions x=5+2*7/3
NOT A
Using the quadratic formula to solve x2 = 5 - x, what are the values of x?
NOT B
Which equation could generate the curve in the graph below?
NOT D (y = 3x2 - 4x - 2)
Study the solutions of the three equations on the right. Then, complete the statements below. There are two real solutions if the radicand is There is one real solution if the radicand is There are no real solutions if the radicand is
Positive Zero Negative
Is the solution shown below correct? Explain. 9x+2=8x2+6x
Sample Response/Explanation: No. The correct values of a, b, and c were substituted in, but the formula was simplified wrong. The 64 should be added so the radicand is 73. There should be 2 real roots.
Select the graphs that have an equation with a < 0.
Second and Third Graph
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 of the statements about the following quadratic equation is true?6x2 - 8 = 4x2 + 7x The discriminant is greater than zero, so there are two real roots. The discriminant is greater than zero, so there are two complex roots. The discriminant is less than zero, so there are two real roots. The discriminant is less than zero, so there are two complex roots.
The discriminant is greater than zero, so there are two real roots.
If the domain of the square root function f(x) is x <_7, which statement must be true?
The x-term inside the radical has a negative coefficient.
If the discriminant of a quadratic equation is equal to , 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.
Choose the graph of y = (x - 3)^2 + 1.
Third Graph
Which equation shows the quadratic formula used correctly to solve 5x2 + 3x - 4 = 0 for x?
a
Which of the statements about the following quadratic equation is true? 6x2 - 8 = 4x2 + 7x
a
Use the discriminant to answer the questions. 32x - 4 = 4x2 + 60For the equation shown, choose the description of the solutions. y - 5 = 0.5x2 + 6x - 3How many x-intercepts does the graph of this quadratic have?
a a
(1) The graph of g(x) = (x + 2)^2 is a translation of the graph of f(x) __(a)__ by __(b)__ units. (2) The graph of h(x) = (x − 3)^2 is a translation of the graph of f(x) __(c)__ by __(d)__ units.
a. left b. 2 c. right d. 2
(1) The graph of g(x) = x2 + 2 is a translation of the graph of f(x) __(a)__ by __(b)__ units. (2) The graph of h(x) = x2 − 3 is a translation of the graph of f(x) __(c)__ by __(d)__ units.
a. up b. 2 c. down d. 3
The height h (in feet) of an object t seconds after it is dropped can be modeled by the quadratic equationh = -16t2 + h0, where h0 is the initial height of the object. Suppose a small rock dislodges from a ledge that is 255 ft above a canyon floor. Solve the equation h = -16t2 + 255 for t, using the quadratic formula to determine the time it takes the rock to reach the canyon floor.
b
When deriving the quadratic formula by completing the square, what expression can be added to both sides of the equation to create a perfect square trinomial? x^2+ (b/a)x +_ = (-c/a)+_
b^2/ 4a^2
Which equation has the solutions ?
c
Solve 0 = 4x2+12x+9. Select the equation that shows the correct substitution of a, b, and c in the quadratic formula. Simplify the expression to solve the equation.
c -1.5
What values of c and d would makethe following expression represent a real number?i(2 + 3i)(c + di) c = 2, d = 3 c = -2, d = 3 c = 3, d = -2 c = -3, d = -2
c = -3, d = -2
Which property of multiplication is shown below?If x = a + bi and y = c + di, x × y = y × x. commutative property identity property distributive property associative property
commutative property
property
commutative: x+y=y+x xy=yx associative:(x+y)+z=x+(y+z) (xy)z=x(yz) distributive: x(y+z)=xy+xz identity: x+0=x 1x=x inverse: x+(-x)=0 x(1/x)=1 (3 + 7i) + (8 − 6i) as (8 − 6i) + (3 + 7i) commutative [(3 + 7i) + (8 − 6i)] + (1+ 9i) as (3 + 7i) + [(8 − 6i) + (1 + 9i)]? associative The distributive property allows 3i + 2i to be written as (3 + 2)i. ai+bi=(a+b)i Which property allows you to write the expression as 5 − 2i − 1 − 8i? distributive additive inverse of -2+8i is 2-8i Which of the following is equivalent to -2i(6 - 7i)?(0 - 2i)(6 - 7i)
Given y = (2x + 3)2, choose the standard form of the given quadratic equation. Identify the values of a, b, and c.
d 4 12 9
Solve each of the quadratic equations. 3x = 0.5x2 0 = 5x2 - 2x + 6
d c
Which could be the function graphed below?
f(x)=√x -2
Which expression is equivalent to i^233? 1 -1 i -i
i
powers of i
i=i, i^2=-1. i^3=-i, i^4=1, i^5=i, i^6=-1. i^7=-i, i^8=1 i^15=(i^4)^3*i^3 a+bi on graph is (a,b) [2]=2, [-3.5]=3.5, [2i]=2, [-1/2 i]=1/2 absolute value The absolute value of any complex number a + bi is the distance from (a, b) to (0, 0) in the complex plane. Because [a + bi] is equal to a distance, [a + bi] will always be a positive real number. distance formula: d = √[( x₂ - x₁)² + (y₂ - y₁)²]
Which property of addition is shown in the equation below?a + bi + 0 + 0i = a + bi commutative property inverse property identity property associative property
identity property
Which property of addition is shown below?If x = a + bi and y = -a - bi, x + y = 0. commutative property identity property associative property inverse property
inverse property
Determine the number of real solutions each quadratic equation has. y = 12x2 - 9x + 4 10x + y = -x2 + 2 4y - 7 = 5x2 - x + 2 + 3y y = (-x + 4)2
no two no one
numbers
real numbers(natural numbers[0-10]inegers[negative]rational numbers[1/2]irrational numbers[pie or squared])imaginary numbers(bi[b real and i is square root -1])
To obtain the graph of y = (x - 8)2, shift the graph of y = x2 updownleftright units. To obtain the graph of y = x2 - 6, shift the graph of y = x2 up downleftright units.
right, 8 / down, 6
What is the distance from the origin to point A graphed on the complex plane below? squareroot 5 squareroot 13 9 13
squareroot 13
If f(x) = 1 - x, which value is equivalent to |f(i)|? 0 1 squareroot 2 squareroot -1
squareroot 2
Fill in the missing steps for the derivation of the quadratic formula using the choices below. Step 1: ax2 + bx + c = 0 Step 2: ax2 + bx = −c Step 3: Step 4:-------------- Step 5: Step 6: Step 7:-------------- Step 8:
step 3: B step 5: D step 6: A step 8: C
The graph of y = -0.2x2 is X narrower than and opens in the same direction asX wider than and opens in the same direction asnarrower than and opens in the opposite direction of wider than and opens in the opposite direction of the graph of y = x2. The graph of y = 5x2 is narrower than and opens in the same direction aswider than and opens in the same direction asX narrower than and opens in the opposite direction ofwider than and opens in the opposite direction of the graph of y = x2.
wider than and opens in the opposite direction of the graph of / narrower than and opens in the same direction as
Solve for in the equation . x^2+20x+100=36 x = -16 or x = -4 x = -10 x = -8 x = 4 or x = 16
x = -16 or x = -4
Solve for in the equation .x^2+14x+17=-96 x= -7 plus minus 4 squareroot 6i x = -7 ± 8i x= 7 plus minus 4 squareroot 6i x = 7 ± 8i
x = -7 ± 8i
3x = 0.5x2 x = -6 or x = 0 x = -4 or x = 3 x = -2 or x = 1.5 x = 0 or x = 6
x = 0 or x = 6
Given (x - 7)2 = 36, select the values of x. x = 13 x = 1 x = -29 x = 42
x = 13 x = 1
Which equation can be simplified to find the inverse of y = 2x2?
x = 2y2
Which equation can be simplified to find the inverse of y = 5x2 + 10?
x = 5y2 + 10
What is the domain of the function y= sqaureroot x+ 6-7
x greater or equal to -6
In the derivation of the quadratic formula by completing the square, the equation(x+(b/2a))^2 = (-4ac+b^2)/ (4a^2) is created by forming a perfect square trinomial.What is the result of applying the square root property of equality to this equation?
x+ (b/2a) = (plus minus squareroot b^2 -4ac) / 2a
If , f(x)= squareroot x-3 which inequality can be used to find the domain of f(x)?
x-3 greater or equal to 0
If f(x)=√x-3, which inequality can be used to find the domain of f(x)?
x-3>_ 0
Which equation shows the quadratic formula used correctly to solve 5x^2 + 3x - 4 = 0 for x?
x= (-3 plus minus squareroot (3)^2-4(5)(-4)/ 2(5)
Solve for in the equation x^2+2x+1=17
x= -1 plus minus squreroot 17
0 = 5x2 - 2x + 6
x= 1 plus minus i squareroot 29 / 5
Use completing the square to solve for in the equation .(x+7)(x-9)=25 x = -4 or 6 x = -2 or 14 x= 1 plus minus squareroot 89 x= 1 plus minus squareroot 87
x= 1 plus minus squareroot 89
Given (x - 1)2 = 50, select the values of x. x = -49 x = 51 x= 1+5 squareroot 2 x= 1-5 squareroot 2
x= 1+5 squareroot 2 x= 1-5 squareroot 2
Solve for x in the equation x^2-12x+59=0
x= 6 plus minus squareroot 23i
What are the solutions of x^2+6x-6=10 x=-11 or x=1 x=-11 or x=-1 x=-8 or x=-2 x=-8 or x=2
x=-8 or x=2
Which equation can be simplified to find the inverse of y = 2x^2?
x=2y^2
Solve for in the equation x^2-10x+25=35
x=5 plus minus squareroot 35
Which equation can be simplified to find the inverse of y = 5x^2 + 10?
x=5y^2+10
What is the domain of the function y=√x+6 -7?
x>_ -6
What is the domain of the square root function graphed below?
x>_3
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 = (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 equation is y = -3x2 - 12x - 2 rewritten in vertex form? y = -3(x + 2)2 + 10 y = -3(x - 2)2 + 10 y = -3(x + 2)2 - 14 y = -3(x - 2)2 - 2
y = -3(x + 2)2 + 10
Which equation is y = -3x² - 12x - 2 rewritten in vertex form?
y = -3(x + 2)² + 10
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
Which equation is y = (x + 3)2 + (x + 4)2 rewritten in vertex form? y=2 (x+ (7/2))- 1/4 y=2 (x+ (7/2))+ 1/4 y = 2(x + 7)2 - 73 y = (x + 7)2 - 24
y=2 (x+ (7/2))+ 1/4
square
√ab=√a√b=√a/b=√a/√b or √9=3 or √16/25=4/5 quadratic equation: y=ax^2+bx+c or 0=ax^2+bx+c quadratic formula:x=-b+-√b^2-4ac /2a There are two real solutions if the radicand is positive. There is one real solution if the radicand is zero. There are no real solutions if the radicand is negative. inverse:f(x)=x^2, y=x^2 and x=y^2,square it
Simplify each of the following powers of i. = i✔ -i1-1 = i-i✔ 1-1 = i✔ -i1-1 = i-i1✔ -1
.
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
Find the sum of (-4 + i) and (10 - 5i). -3 + 5i -3 - 5i 6 - 4i 6 - 6i
6 - 4i
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 first step when rewriting y = 6x² + 18x + 14 in the form y = a(x - h)² + k?
6 must be factored from 6x² + 18x
Solve x2 - 16x + 60 = -12 by completing the steps. First, subtract _____from each side of the equation. Next, add ____to each side of the equation to complete the square.
60 64
Which value must be added to the expression x2 + 16x to make it a perfect-square trinomial? 8 32 64 256
64
Find the discriminant of 3x^2-10x=-2
76
What is the discriminant of ?
76
Now, write x² - 16x + 64 = -8 as ✔ (x - 8)² = -8
8 2
Brian is solving the equation x^2- (3/4)x = 5 What value must be added to both sides of the equation to make the left side a perfect-square trinomial?
9/64
The graph of an equation with a negative discriminant always has which characteristic?
A)no x-intercept
Which equation is y = (x + 3)2 + (x + 4)2 rewritten in vertex form?
A.
Which equation has a graph that is a parabola with a vertex at (5, 3)?
A. y = (x - 5)2 + 3
Which equation is the inverse of y = 2x2 - 8?
A. y= squaretoot x=8/2
Which expression is equivalent to squareroot -80 ? -4 squareroot 5 -4 squareroot 5i 4 squareroot 5i 4 squareroot 5
4 squareroot 5i
What is the first step when rewriting y = -4x2 + 2x - 7 in the form y = a(x - h)2 + k?
B. -4 must be factored from -4x2 + 2x
How does the graph of y = a(x - h)2 + k change if the value of h is doubled?
B. The vertex of the graph moves to a point twice as far from the y-axis.
Which pair of equations generates graphs with the same vertex?
B. y = -4x2 and y = 4x2
Which of following is the graph of y = -(x + 1)2 -3?
C
Which phrase best describes the translation from the graph y = 6x2 to the graph of y = 6(x + 1)2?
C. 1 unit left
Which phrase best describes the translation from the graph y = (x + 2)2 to the graph of y = x2 + 3?
C. 2 units right and 3 units up
Which equation is y = 2x2 - 8x + 9 rewritten in vertex form?
C. y = 2(x - 2)2 + 1
Which equation is the inverse of y = 16x2 + 1?
y= squareoot x-1/4
Which equation is the inverse of 5y+4=(x+3)^2+1/2
y=-3+-√5x+(7/2
Which equation is the inverse of 2(x - 2)2 = 8(7 + y)?
y=2 +_ squareroot 28+4x
y = 12x2 - 9x + 4✔ no real solution(s) 10x + y = -x2 + 2✔ two real solution(s) 4y - 7 = 5x2 - x + 2 + 3y✔ no real solution(s) y = (-x + 4)2X ✔ one real solution(s)
.
√−100 = + i
0 + 10 i
Aiko is finding the sum (4 + 5i) + (-3 + 7i). She rewrites the sum as (-3 + 7)i + (4 + 5)i. Which statement explains the error Aiko made by using a mathematical property incorrectly? Aiko incorrectly used the commutative property by changing the order of the two complex numbers. Aiko incorrectly used the associative property by changing the order of the two complex numbers. Aiko incorrectly used the identity property by combining the real number and the coefficient of the imaginary part. Aiko incorrectly used the distributive property by combining the real number and the coefficient of the imaginary part.
Aiko incorrectly used the distributive property by combining the real number and the coefficient of the imaginary part.
Using the quadratic formula to solve 5x = 6x2 - 3, what are the values of x?
B
Using the quadratic formula to solve 7x2 - x = 7, what are the values of x?
B
Complete the statements. Graph has one real root. Graph has a negative discriminant. Graph has an equation with coefficients a = 1, b = 4, c = -2
B A C
Which of the following transforms to the graph of ? a translation 5 units to the right a translation 5 units to the left a translation 5 units down a translation 5 units up Which of the following transforms the graph of to the graph of ? a translation 7 units to the right a translation 7 units to the left translation 7 units down a translation 7 units up
B / C
Which of the following statements are true about the graph of f(x) = 6(x + 1)2 -9?Check all of the boxes that apply. The vertex is (1, -9). The graph opens upward. The graph is obtained by shifting the graph of f(x) = 6(x + 1)2 up 9 units. The graph is steeper than the graph of f(x) = x2. The graph is the same as the graph of f(x) = 6x2 + 12x - 3.
B, D, E
A ball is thrown straight up from a height of 3 ft with a speed of 32 ft/s. Its height above the ground after x seconds is given by the quadratic function y = -16x2 + 32x + 3. Explain the steps you would use to determine the path of the ball in terms of a transformation of the graph of y = x2.
Complete the square to get the equation in vertex form witha = -16, h = 1, and k = 19. The path is a reflection over the x-axis and narrower. It is also translated right 1 unit and up 19 units.
Which equation has a graph that is a parabola with a vertex at (-1, -1)?
D. y = (x + 1)2 - 1
(1) Compare the graphs of the functions listed below. Function 1: y = 0.25x^2 Function 2: y = 4x^2 Function 3: y = -½x^2 Function 4: y = -16x^2 The graph of __(a)__ is the widest. The graph of __(b)__ is the narrowest. The graph of function 2 is __(c)__ the graph of function 3.
a. function 1 b. function 4 c. narrower than
Choose the equation that represents the solutions of 0 = 0.25x2 - 8x.
c
The height h (in feet) of an object t seconds after it is dropped can be modeled by the quadratic equationh = -16t2 + h0, where h0 is the initial height of the object. Suppose a small rock dislodges from a ledge that is 255 ft above a canyon floor. Solve the equation h = -16t2 + 255 for t, using the quadratic formula to determine the time it takes the rock to reach the canyon floor. t 0.87 s t 4 s t = 8.5 s t = 16 s
t=4 s
Christian is rewriting an expression of the form y = ax² + bx + c in the form y = a(x - h)² + k. Which of the following must be true?
the value of a remains the same
Solve for in the equation . x^2+10x+12=36 x = -12 or x = 2 x = -11 or x = 1 x = -2 or x = 12 x = -1 or x = 11
x = -12 or x = 2
