Quadratic Functions Unit Test

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

Vertex of a quadratic function (formula)

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

x = 2 Vertex: (2, 4)

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

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

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

Consider the graph of the function f(x) = 2(x + 3)2 + 2. Over which interval is the graph decreasing?
(-∞, -3)
(-∞, 2)
(-3, ∞)
(2, ∞)

(-∞, -3)

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.

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

The graph of which function is decreasing over the interval (-4, ∞)?

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

f(x) = (x – 4)2 – 4 – INCORRECT

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

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

(-8, ∞)

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

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

f(x) = -(x – 4)2 + 5

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

The graph of f(x) = x2 is translated to form
g(x) = (x – 2)2 – 3.
Which graph represents g(x)?

A

Sanjay begins to correctly graph the function f(x) = (x + 1)2 – 3. Based on the axis of symmetry and the vertex, which graph could be Sanjay’s?

C

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

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)

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)

Which function has two x-intercepts, one at (0, 0) and one at (4, 0)?

f(x) = x(x − 4)
f(x) = x(x + 4)
f(x) = (x − 4)(x − 4)
f(x) = (x + 4)(x + 4)

f(x) = x(x − 4)

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)

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

The axis of symmetry is x =

6

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.

Which is the graph of f(x) = -(x + 3)(x + 1)?

B

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 &lt; -4.
The function is increasing for all real values of x where
-6 &lt; x &lt; -2.
The function is decreasing for all real values of x where
x &lt; -6 and where x &gt; -2.
The function is decreasing for all real values of x where
x &lt; -4.

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

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

The axis of symmetry for the function f(x) = −x2 − 10x + 16 is x = −5. What are the coordinates of the vertex of the graph?

(−5, 41)
(−5, 56)
(−5, 76)
(−5, 91)

(−5, 41)

The axis of symmetry for a function in the form f(x) = x2 + 4x − 5 is x = −2. What are the coordinates of the vertex of the graph?

(−9, −2)
(−17, −2)
(−2, −17)
(−2, −9)

(−2, −9)

The graph of which function has a y-intercept of 3?

A

Which is the graph of f(x) = x2 – 2x + 3?

NOT C, C IS INCORRECT

The graph of which function has an axis of symmetry at x = 3?

d

The axis of symmetry for the graph of the function f(x) = 3×2 + bx + 4 is x = . What is the value of b?

-9

Tempestt graphs a function that has a maximum located at (-4, 2). Which could be her graph?

C

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)

liana started to evaluate the function f(x) = 2×2 – 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

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

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

Which quadratic function is represented by the table?

f(x) = 3×2 + 2x – 5
f(x) = 3×2 – 2x + 5
f(x) = 2×2 + 3x – 5
f(x) = 2×2 – 2x + 5

f(x) = 3×2 – 2x + 5

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

6

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

1

Which quadratic function has a leading coefficient of 2 and a constant term of -3?

f(x) = 2×3 – 3
f(x) = -3×2 – 3x + 2
f(x) = -3×3 + 2
f(x) = 2×2 + 3x – 3

f(x) = 2×2 + 3x – 3

Which represents a quadratic function?

f(x) = 2×3 + 2×2 – 4
f(x) = -7×2 – x + 2
f(x) = -3x + 2
f(x) = 0x2 + 3x – 3

f(x) = -7×2 – x + 2

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) = x² left 10 units and down 117 units.

The function g(x) = 3×2 − 12x + 7 written in vertex form is g(x) = 3(x − 2)2 − 5. What is the vertex of g(x)?

(−6, −5)

(−2, −5)
(2, −5)
(6, −5)

(2, −5)

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

The function h(x) = -2×2 + 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.

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

The function g(x) = -3×2 – 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) = -3×2 – 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.

Which is one of the transformations applied to the graph of f(x) = x2 to change it into the graph of g(x) = 4×2 + 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.

What is f(x) = 8×2 + 4x written in vertex form?

f(x) = 8 –
f(x) = 8 –
f(x) = 8 – 2
f(x) = 8 – 4

A

What is f(x) = 2×2 + 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

The first three steps in writing f(x) = 40x + 5×2 in vertex form are shown.

Write the function in standard form. f(x) = 5×2 + 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

The function g(x) = 10×2 – 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.

Which function in vertex form is equivalent to f(x) = x2 + 6x + 3?

f(x) = (x + 3)2 + 3
f(x) = (x + 3)2 − 6
f(x) = (x + 6)2 + 3
f(x) = (x + 6)2 − 6

f(x) = (x + 3)2 − 6

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

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

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

16

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)

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, ).

What value for c will make the expression a perfect square trinomial?

x2 – 7x + c

49/4

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.

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

1

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

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

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)

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

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 ≥ 3}.
The range is {y| y ≥ -1}.
The function decreases over the interval (-∞, 3).
The function increases over the interval (-1, ∞).
The axis of symmetry is x = -1.
The vertex is (3, -1).

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

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)

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 − 7)2 − 3
g(x) = (x + 7)2 − 3
g(x) = (x − 3)2 − 7
g(x) = (x − 3)2 + 7

g(x) = (x + 7)2 − 3

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

The graph of the function f(x) = (x + 2)(x − 4) is shown.

Which describes all of the values for which the graph is negative and increasing?

all real values of x where x &lt; −2
all real values of x where −2 &lt; x &lt; 4
all real values of x where 1 &lt; x &lt; 4
all real values of x where x &lt; 0

all real values of x where 1 < x < 4

What is the axis of symmetry of h(x) = 6×2 − 60x + 147?

x = −5
x = −3
x = 3
x = 5

x = 5

Which translation maps the graph of the function f(x) = x2 onto the function g(x) = x2 − 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

right 3 units, down 3 units

The graph of the function f(x) = −3×2 − 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 (−2, 0) and (1,0).
The function is decreasing from (−∞, 6.75).

The vertex is the maximum value. The axis of symmetry is x = . The domain is all real numbers. The x-intercepts are at (−2, 0) and (1,0).

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

The y-value of the vertex is

49

What are the x-intercepts of the graph of the function f(x) = x2 + 5x − 36?

(−4, 0) and (9, 0)
(4, 0) and (−9, 0)
(−3, 0) and (12, 0)
(3, 0) and (−12, 0)

(4, 0) and (−9, 0)