question

f(x)=a(x-h)^2+k

answer

Vertex of a quadratic function (formula)

question

What is the axis of symmetry and vertex for the function f(x) = 3(x - 2)2 + 4?

answer

x = 2
Vertex: (2, 4)

question

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

answer

right 3 units, down 1 unit

question

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 +

answer

9
-8

question

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

answer

f(x) = (x + 1)2 + 5

question

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)

answer

(-β, -3)

question

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.

answer

The domain is all real numbers.
The y-intercept is 3.

question

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

answer

left 13 units, down 2 units

question

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

answer

g(x) = (x - 5)2 + 2

question

Over what interval is the graph of f(x) = -(x + 8)2 - 1 decreasing?

answer

(-8, β)

question

Which best describes the transformation that occurs from the graph of f(x) = x2 to g(x) = (x - 2)2 + 3?

answer

right 2, up 3

question

Which function has a range of {y|y β€ 5}?

answer

f(x) = -(x - 4)2 + 5

question

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?

answer

3

question

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

answer

f(x) = (x - 8)2 - 6

question

What is the y-intercept of the quadratic function
f(x) = (x - 8)(x + 3)?
(8,0)
(0,3)
(0,-24)
(-5,0)

answer

(0,-24)

question

What is the midpoint of the x-intercepts of
f(x) = (x - 2)(x - 4)?
(-3,0)
(-1,0)
(1,0)
(3,0)

answer

(3,0)

question

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)

answer

f(x) = x(x β 4)

question

Which point is an x-intercept of the quadratic function
f(x) = (x + 6)(x - 3)?
(0,6)
(0,-6)
(6,0)
(-6,0)

answer

(-6,0)

question

What is the axis of symmetry of the function f(x) = -(x + 9)(x - 21)?
The axis of symmetry is x =

answer

6

question

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.

answer

The function is decreasing for all real values of x where
x < 1.5.

question

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.

answer

The function is increasing for all real values of x where
x < -4.

question

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?

answer

-3

question

The axis of symmetry for the function f(x) = βx2 β 10x + 16 is x = β5. What are the coordinates of the vertex of the graph?
(β5, 41)
(β5, 56)
(β5, 76)
(β5, 91)

answer

(β5, 41)

question

The axis of symmetry for a function in the form f(x) = x2 + 4x β 5 is x = β2. What are the coordinates of the vertex of the graph?
(β9, β2)
(β17, β2)
(β2, β17)
(β2, β9)

answer

(β2, β9)

question

The axis of symmetry for the graph of the function f(x) = 3x2 + bx + 4 is x = . What is the value of b?

answer

-9

question

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)

answer

(-6, 0), (2,0)

question

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

answer

9

question

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

answer

-4c2 + 4c + 6

question

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

answer

A = 4, B = 3

question

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

answer

f(x) = 3x2 - 2x + 5

question

Consider the quadratic function f(y) = 8y2 - 7y + 6. What is the constant of the function?

answer

6

question

What is f(-3) for the function f(a) = -2a2 - 5a + 4?

answer

1

question

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

answer

f(x) = 2x2 + 3x - 3

question

Which represents a quadratic function?
f(x) = 2x3 + 2x2 - 4
f(x) = -7x2 - x + 2
f(x) = -3x + 2
f(x) = 0x2 + 3x - 3

answer

f(x) = -7x2 - x + 2

question

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.

answer

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.

question

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)?
(β6, β5)
(β2, β5)
(2, β5)
(6, β5)

answer

(2, β5)

question

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.

answer

The graph of f(x) = x2 is reflected over t

question

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.

answer

The vertex is at (2, 8) and the axis of symmetry is x = 2.

question

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

answer

g(x) = 8(x2 - 6x + 9) - 5

question

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.

answer

The graph of f(x) = x2 is made narrower.

question

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.

answer

The graph of f(x) = x2 is shifted left 3 units.

question

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

answer

f(x) = 2(x + 7)2 - 103

question

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

answer

f(x) = 5(x + 4)2 - 80

question

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.

answer

The vertex of the graph is (5, -37).
The parabola has a minimum.
The parabola opens up.

question

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

answer

f(x) = (x + 3)2 β 6

question

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

answer

36, -36

question

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

answer

f(x) = (x - 1)2 + 3

question

Which value is needed to create a perfect square trinomial from the expression x2 + 8x + _____?

answer

16

question

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)

answer

(-5, -28)

question

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.

answer

The vertex of the function is (-3, -13).
The graph increases over the interval (-3, ).

question

What value for c will make the expression a perfect square trinomial?
x2 - 7x + c

answer

49/4

question

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.

answer

The x-coordinate of the vertex is greater than the y-coordinate.

question

How many unit tiles need to be added to the expression
x2 + 4x + 3 in order to form a perfect square trinomial?

answer

1

question

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

answer

right 4, down 9

question

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

answer

g(x) = (x - 2)2 + k

question

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)

answer

f(x)= (x-2)(x+2)

question

What is the y-value of the vertex of the function f(x) = -(x + 8)(x - 14)?
The y-value of the vertex is

answer

y = 121

question

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).

answer

The range is {y| y β₯ -1}.
The function decreases over the interval (-β, 3).
The vertex is (3, -1).

question

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)

answer

f(x) = (x - 2)(x + 2)

question

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

answer

g(x) = (x + 7)2 β 3

question

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

answer

right 5, down 23

question

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 < β2
all real values of x where β2 < x < 4
all real values of x where 1 < x < 4
all real values of x where x < 0

answer

all real values of x where 1 < x < 4

question

What is the axis of symmetry of h(x) = 6x2 β 60x + 147?
x = β5
x = β3
x = 3
x = 5

answer

x = 5

question

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

answer

right 3 units, down 3 units

question

The graph of the function f(x) = β3x2 β 3x + 6 is shown. Which statements describe the graph? Check all that apply.
The vertex is the maximum value.
The axis of symmetry is x = .
The domain is all real numbers.
The range is all real numbers.
The x-intercepts are at (β2, 0) and (1,0).
The function is decreasing from (ββ, 6.75).

answer

The vertex is the maximum value.
The axis of symmetry is x = .
The domain is all real numbers.
The x-intercepts are at (β2, 0) and (1,0).

question

What is the y-value of the vertex of the function f(x) = -(x - 3)(x + 11)?
The y-value of the vertex is

answer

49

question

What are the x-intercepts of the graph of the function f(x) = x2 + 5x β 36?
(β4, 0) and (9, 0)
(4, 0) and (β9, 0)
(β3, 0) and (12, 0)
(3, 0) and (β12, 0)

answer

(4, 0) and (β9, 0)