## Unlock all answers in this set

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f(x)=a(x-h)^2+k
Vertex of a quadratic function (formula)
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What is the axis of symmetry and vertex for the function f(x) = 3(x - 2)2 + 4?
x = 2 Vertex: (2, 4)
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Which best describes the transformation from the graph of f(x) = x2 to the graph of f(x) = (x - 3)2 - 1? left 3 units, down 1 unit left 3 units, up 1 unit right 3 units, down 1 unit right 3 units, up 1 unit
right 3 units, down 1 unit
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The parent function of the function g(x) = (x - h)2 + k is f(x) = x2. The vertex of the function g(x) is located at (9, -8). What are the values of h and k? g(x) = (x - )^2 +
9 -8
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What is the equation of the translated function? f(x) = (x - 1)2 - 5 f(x) = (x + 1)2 + 5 f(x) = (x - 5)2 - 1 f(x) = (x + 5)2 + 1
f(x) = (x + 1)2 + 5
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Consider the graph of the function f(x) = 2(x + 3)2 + 2. Over which interval is the graph decreasing? (-β, -3) (-β, 2) (-3, β) (2, β)
(-β, -3)
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Which are characteristics of the graph of the function f(x) = (x + 1)2 + 2? Check all that apply. The domain is all real numbers. The range is all real numbers greater than or equal to 1. The y-intercept is 3. The graph of the function is 1 unit up and 2 units to the left from the graph of y = x2. The graph has two x-intercepts.
The domain is all real numbers. The y-intercept is 3.
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Justine graphs the function f(x) = (x - 7)2 - 1. On the same grid, she graphs the function g(x) = (x + 6)2 - 3. Which transformation will map f(x) on to g(x)? left 13 units, down 2 units right 13 units, down 2 units left 13 units, up 2 units right 13 units, up 2 units
left 13 units, down 2 units
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What is the equation of the translated function, g(x), if f(x) = x2? g(x) = (x + 5)2 + 2 g(x) = (x + 2)2 + 5 g(x) = (x - 2)2 + 5 g(x) = (x - 5)2 + 2
g(x) = (x - 5)2 + 2
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Over what interval is the graph of f(x) = -(x + 8)2 - 1 decreasing?
(-8, β)
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Which best describes the transformation that occurs from the graph of f(x) = x2 to g(x) = (x - 2)2 + 3?
right 2, up 3
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Which function has a range of {y|y β€ 5}?
f(x) = -(x - 4)2 + 5
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What value represents the vertical translation from the graph of the parent function f(x) = x2 to the graph of the function g(x) = (x + 5)2 + 3?
3
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Which function could be represented by the graph on the coordinate plane? f(x) = (x - 8)2 + 6 f(x) = (x + 8)2 + 6 f(x) = (x + 8)2 - 6 f(x) = (x - 8)2 - 6
f(x) = (x - 8)2 - 6
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What is the y-intercept of the quadratic function f(x) = (x - 8)(x + 3)? (8,0) (0,3) (0,-24) (-5,0)
(0,-24)
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What is the midpoint of the x-intercepts of f(x) = (x - 2)(x - 4)? (-3,0) (-1,0) (1,0) (3,0)
(3,0)
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Which function has two x-intercepts, one at (0, 0) and one at (4, 0)? f(x) = x(x β 4) f(x) = x(x + 4) f(x) = (x β 4)(x β 4) f(x) = (x + 4)(x + 4)
f(x) = x(x β 4)
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Which point is an x-intercept of the quadratic function f(x) = (x + 6)(x - 3)? (0,6) (0,-6) (6,0) (-6,0)
(-6,0)
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What is the axis of symmetry of the function f(x) = -(x + 9)(x - 21)? The axis of symmetry is x =
6
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The graph of the function f(x) = (x - 4)(x + 1) is shown below. Which statement about the function is true? The function is increasing for all real values of x where x < 0. The function is increasing for all real values of x where x < -1 and where x > 4. The function is decreasing for all real values of x where -1 < x < 4. The function is decreasing for all real values of x where x < 1.5.
The function is decreasing for all real values of x where x < 1.5.
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The graph of the function f(x) = -(x + 6)(x + 2) is shown below. Which statement about the function is true? The function is increasing for all real values of x where x < -4. The function is increasing for all real values of x where -6 < x < -2. The function is decreasing for all real values of x where x < -6 and where x > -2. The function is decreasing for all real values of x where x < -4.
The function is increasing for all real values of x where x < -4.
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The axis of symmetry for the graph of the function is f(x) = x2 + bx + 10 is x = 6. What is the value of b?
-3
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The axis of symmetry for the function f(x) = βx2 β 10x + 16 is x = β5. What are the coordinates of the vertex of the graph? (β5, 41) (β5, 56) (β5, 76) (β5, 91)
(β5, 41)
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The axis of symmetry for a function in the form f(x) = x2 + 4x β 5 is x = β2. What are the coordinates of the vertex of the graph? (β9, β2) (β17, β2) (β2, β17) (β2, β9)
(β2, β9)
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The axis of symmetry for the graph of the function f(x) = 3x2 + bx + 4 is x = . What is the value of b?
-9
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What are the x-intercepts of the graph of the function f(x) = x2 + 4x - 12? (-6, 0), (2,0) (-2, -16), (0, -12) (-6, 0), (-2, -16), (2, 0) (0, -12), (-6, 0), (2, 0)
(-6, 0), (2,0)
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liana started to evaluate the function f(x) = 2x2 - 3x + 7 for the input value 2. f(x) = 2(2)2 - 3(2) + 7 = 2(4) - 3(2) + 7 What is the value of the function when x = 2? 9 10 16 17
9
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When simplified and written in standard form, which quadratic function is equivalent to the polynomial shown? 2 + 7c - 4c2 - 3c + 4 -4c2 + 4c + 6 -7c2 + 10c + 6 -4c2 + 4c + 8 -7c2 + 7c + 6
-4c2 + 4c + 6
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1 2 3 5 6 8 9 10 Mary throws a plastic disc to her friend, which her friend catches six seconds after Mary throws it. The table shows the height of the disc at one-second intervals. Assuming that the throw represents projectile motion, what are the missing values in the table? A = 5, B = 3 A = 4, B = 0 A = 4, B = 3 A = 5, B = 0
A = 4, B = 3
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Which quadratic function is represented by the table? f(x) = 3x2 + 2x - 5 f(x) = 3x2 - 2x + 5 f(x) = 2x2 + 3x - 5 f(x) = 2x2 - 2x + 5
f(x) = 3x2 - 2x + 5
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Consider the quadratic function f(y) = 8y2 - 7y + 6. What is the constant of the function?
6
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What is f(-3) for the function f(a) = -2a2 - 5a + 4?
1
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Which quadratic function has a leading coefficient of 2 and a constant term of -3? f(x) = 2x3 - 3 f(x) = -3x2 - 3x + 2 f(x) = -3x3 + 2 f(x) = 2x2 + 3x - 3
f(x) = 2x2 + 3x - 3
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Which represents a quadratic function? f(x) = 2x3 + 2x2 - 4 f(x) = -7x2 - x + 2 f(x) = -3x + 2 f(x) = 0x2 + 3x - 3
f(x) = -7x2 - x + 2
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What is true about the function h(x) = x2 + 20x - 17? Check all that apply. The vertex of h is (-10, -117). The vertex form of the function is h(x) = (x + 20)2 - 17. The maximum value of the function is -17. To graph the function h, shift the graph of f(x) = x2 left 10 units and down 117 units. The axis of symmetry of function h is x = 20.
The vertex of h is: (-10, -117). To graph the function h, shift the graph of f(x) = xΒ² left 10 units and down 117 units.
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The function g(x) = 3x2 β 12x + 7 written in vertex form is g(x) = 3(x β 2)2 β 5. What is the vertex of g(x)? (β6, β5) (β2, β5) (2, β5) (6, β5)
(2, β5)
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The function g(x) = -x2 + 16x - 44 written in vertex form is g(x) = -(x - 8)2 + 20. Which is one of the transformations applied to the graph of f(x) = x2 to change it into the graph of g(x) = -x2 + 16x - 44? The graph of f(x) = x2 is widened. The graph of f(x) = x2 is shifted left 8 units. The graph of f(x) = x2 is shifted down 44 units. The graph of f(x) = x2 is reflected over the x-axis.
The graph of f(x) = x2 is reflected over t
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The function h(x) = -2x2 + 8x written in vertex form is h(x) = -2(x - 2)2 + 8. The function h(x) is shown on the graph along with the parent function, f(x) = x2. Which statement is true concerning the vertex and axis of symmetry of h(x)? The vertex is at (0, 0) and the axis of symmetry is x = 2. The vertex is at (0, 0) and the axis of symmetry is y= 2. The vertex is at (2, 8) and the axis of symmetry is x = 2. The vertex is at (2, 2) and the axis of symmetry is y = 2.
The vertex is at (2, 8) and the axis of symmetry is x = 2.
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Which function has a minimum and is transformed to the right and down from the parent function, f(x) = x2? g(x) = -9(x2 + 2x + 1) - 7 g(x) = 4(x2 - 6x + 9) + 1 g(x) = -3(x2 - 8x + 16) - 6 g(x) = 8(x2 - 6x + 9) - 5
g(x) = 8(x2 - 6x + 9) - 5
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The function g(x) = -3x2 - 36x - 60 written in vertex form is g(x) = -3(x + 6)2 + 48. Which is one of the transformations applied to the graph of f(x) = x2 to change it into the graph of g(x) = -3x2 - 36x - 60? The graph of f(x) = x2 is made narrower. The graph of f(x) = x2 is shifted right 6 units. The graph of f(x) = x2 is shifted down 48 units. The graph of f(x) = x2 is reflected over the y-axis.
The graph of f(x) = x2 is made narrower.
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Which is one of the transformations applied to the graph of f(x) = x2 to change it into the graph of g(x) = 4x2 + 24x + 30? The graph of f(x) = x2 is widened. The graph of f(x) = x2 is shifted left 3 units. The graph of f(x) = x2 is shifted up 30 units. The graph of f(x) = x2 is reflected over the x-axis.
The graph of f(x) = x2 is shifted left 3 units.
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What is f(x) = 2x2 + 28x - 5 written in vertex form? f(x) = 2(x + 7)2 - 19 f(x) = 2(x + 7)2 - 103 f(x) = 2(x + 14)2 - 14 f(x) = 2(x + 14)2 - 98
f(x) = 2(x + 7)2 - 103
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The first three steps in writing f(x) = 40x + 5x2 in vertex form are shown. Write the function in standard form. f(x) = 5x2 + 40x Factor a out of the first two terms. f(x) = 5(x2 + 8x) Form a perfect square trinomial. = 16 f(x) = 5(x2 + 8x + 16) - 5(16) What is the function written in vertex form? f(x) = 5(x + 4) - 80 f(x) = 5(x + 8) - 80 f(x) = 5(x + 4)2 - 80 f(x) = 5(x + 8)2 - 80
f(x) = 5(x + 4)2 - 80
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The function g(x) = 10x2 - 100x + 213 written in vertex form is g(x) = 10(x - 5)2 - 37. Which statements are true about g(x)? Check all that apply. The axis of symmetry is the line x = -5. The vertex of the graph is (5, -37). The parabola has a minimum. The parabola opens up. The value of a, when the equation is written in vertex form, is negative.
The vertex of the graph is (5, -37). The parabola has a minimum. The parabola opens up.
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Which function in vertex form is equivalent to f(x) = x2 + 6x + 3? f(x) = (x + 3)2 + 3 f(x) = (x + 3)2 β 6 f(x) = (x + 6)2 + 3 f(x) = (x + 6)2 β 6
f(x) = (x + 3)2 β 6
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Which zero pair could be added to the function so that the function can be written in vertex form? 3, -3 6, -6 9, -9 36, -36
36, -36
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Which function in vertex form is equivalent to f(x) = 4 + x2 - 2x? f(x) = (x - 1)2 + 3 f(x) = (x - 1)2 + 5 f(x) = (x + 1)2 + 3 f(x) = (x + 1)2 + 5
f(x) = (x - 1)2 + 3
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Which value is needed to create a perfect square trinomial from the expression x2 + 8x + _____?
16
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The function f(x) = x2 + 10x - 3 written in vertex form is f(x) = (x + 5)2 - 28. What are the coordinates of the vertex? (-5, -28) (-5, 28) (5, -28) (5, 28)
(-5, -28)
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Which statements are true about the graph of the function f(x) = 6x - 4 + x2? Check all that apply. The vertex form of the function is f(x) = (x - 2)2 + 2. The vertex of the function is (-3, -13). The axis of symmetry for the function is x = 3. The graph increases over the interval (-3, ). The function does not cross the x-axis.
The vertex of the function is (-3, -13). The graph increases over the interval (-3, ).
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What value for c will make the expression a perfect square trinomial? x2 - 7x + c
49/4
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Charla wants to determine the vertex of the function f(x) = x2 - 18x + 60 by changing the function into vertex form. Which statement about the vertex of the function is true? The x-coordinate of the vertex is greater than the y-coordinate. The x-coordinate of the vertex is negative. The y-coordinate of the vertex is greater than the y-intercept. The y-coordinate of the vertex is positive.
The x-coordinate of the vertex is greater than the y-coordinate.
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How many unit tiles need to be added to the expression x2 + 4x + 3 in order to form a perfect square trinomial?
1
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Which translation maps the vertex of the graph of the function f(x) = x2 onto the vertex of the function g(x) = -8x + x2 + 7 ? left 4, down 9 left 4, up 23 right 4, down 9 right 4, up 23
right 4, down 9
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The function g(x) is a translation of f(x) = (x + 3)2 - 10. The axis of symmetry of g(x) is 5 units to the right of f(x) . Which function could be g(x)? g(x) = (x - 2)2 + k g(x) = (x + 8)2 + k g(x) = (x - h)2 - 5 g(x) = (x - h)2 - 15
g(x) = (x - 2)2 + k
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Which function has a vertex on the y-axis? f(x) = (x - 2)2 f(x) = x(x + 2) f(x) = (x - 2)(x + 2) f(x) = (x + 1)(x - 2)
f(x)= (x-2)(x+2)
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What is the y-value of the vertex of the function f(x) = -(x + 8)(x - 14)? The y-value of the vertex is
y = 121
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Gerald graphs the function f(x) = (x - 3)2 - 1. Which statements are true about the graph? Check all that apply. The domain is {x| x β₯ 3}. The range is {y| y β₯ -1}. The function decreases over the interval (-β, 3). The function increases over the interval (-1, β). The axis of symmetry is x = -1. The vertex is (3, -1).
The range is {y| y β₯ -1}. The function decreases over the interval (-β, 3). The vertex is (3, -1).
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Which function has a vertex on the y-axis? f(x) = (x - 2)2 f(x) = x(x + 2) f(x) = (x - 2)(x + 2) f(x) = (x + 1)(x - 2)
f(x) = (x - 2)(x + 2)
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The function f(x) = x2 is translated 7 units to the left and 3 units down to form the function g(x). Which represents g(x)? g(x) = (x β 7)2 β 3 g(x) = (x + 7)2 β 3 g(x) = (x β 3)2 β 7 g(x) = (x β 3)2 + 7
g(x) = (x + 7)2 β 3
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Which translation maps the vertex of the graph of the function f(x) = x2 onto the vertex of the function g(x) = x2 - 10x +2? right 5, down 23 left 5, down 23 right 5, up 27 left 5, up 27
right 5, down 23
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The graph of the function f(x) = (x + 2)(x β 4) is shown. Which describes all of the values for which the graph is negative and increasing? all real values of x where x < β2 all real values of x where β2 < x < 4 all real values of x where 1 < x < 4 all real values of x where x < 0
all real values of x where 1 < x < 4
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What is the axis of symmetry of h(x) = 6x2 β 60x + 147? x = β5 x = β3 x = 3 x = 5
x = 5
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Which translation maps the graph of the function f(x) = x2 onto the function g(x) = x2 β 6x + 6? left 3 units, down 3 units right 3 units, down 3 units left 6 units, down 1 unit right 6 units, down 1 unit