Free Printable Quadratic Functions Review

1.

Label how each number transforms the function

a)Left 3

b)Moves up 7

c)Reflected over the x-axis

d)Stretched by a factor of 2

e)Right 3

1

2

3

4

1)

2)

3)

4)

2.

The equation $f\left(x\right)=\frac{2}{3}\left(x-4\right)^2+1$ (a) by $\frac{2}{3}$ , (b) 4, and (c) 1.

Choose from the below words

stretches

moves right

moves up

compresses

moves left

moves down

3.

Find the zeroes. x=_ and x=_

(a)

4.

The vertex is (_, _)

(a)

5.

What is the axis of symmetry?

(a)

6.

$f\left(x\right)=\left(x+5\right)^2+4$

7.

Graph $f\left(x\right)=2\left(x-2\right)^2-3$

8.

Graph $f\left(x\right)=\frac{1}{4}\left(x-4\right)^2+3$

9.

Write the function for $x^2$ in vertex form when it is reflected, shifted up 6, and moved right 1

f(x)= (a) (x (b) )^2 (c)

Choose from the below words

-

-1

+6

+1

-6

10.

What is the domain for quadratic equations?

a)

$x\ge0$

b)

$x\ge k$

c)

All Real Numbers

d)

No Solution

11.

Graph $f\left(x\right)=2x^2-4x+5$

12.

Determine the vertex of the parabola:
y = 5x²- 20x + 13

a)

(5, -7)

b)

(-2, -7)

c)

(2, -7)

d)

(-7, -2)

13.

What is the y-intercept?
f(x) = -2x² + 4x - 6

a)

(0, 6)

b)

(0, -6)

c)

(6, 0)

d)

(-6, 0)

14.

What is the range of this quadratic?

a)

y ≥ 3

b)

y ≤ 3

c)

ℝ

d)

y ≤ 2

15.

What is the axis of symmetry for the equation: y = ½(x - 4)² - 4?

a)

y = 4

b)

y = - 4

c)

x = 4

d)

x = - 4

16.

$y=4(x+2)^2-8$

Convert the equation from vertex form to standard form.

a)

$y=4x^2+16x+8$

b)

$y=4x^2+16x+16$

c)

$y=16x^2+64x-8$

d)

$y=16x^2+256x+8$

17.

What is the standard form of a quadratic?

a)

$y=ax^2+bx+c$

b)

$y=mx+b$

c)

$\ -\frac{b}{2a}$

d)

$y=a\left(x-h\right)^2+k$

18.

What is the axis of symmerty of a parabola?

a)

the highest point of a parabola

b)

An imaginary line that cuts the parabola in half

c)

the lowest point of a parabola

d)

where the parabola crosses the y-axis

19.

What equation do we use to find the axis of symmetry?

a)

$y=ax^2+bx+c$

b)

$x=-\frac{b}{2a}$

c)

$y=mx+b$

d)

$y-y_1=m\left(x-x_1\right)$

20.

Find the axis of symmetry for $f\left(x\right)=x^2-8x+15$

Use: $x=-\frac{b}{2a}$

a)

x = 4

b)

x=15

c)

x=-1

d)

x=-8

21.

What is a, b, and c in 3x² -5x+ 4

a)

a = 3, b = -5, c = 4

b)

a = 3, b = 5, c = -4

c)

a = 3, b = 5, c = 4

d)

a = 3, b = -5, c = -4

22.

$f\left(x\right)=x^2+x-2$

Find the axis of symmetry

a)

$x=\frac{1}{2}$

b)

$x=-\frac{1}{2}$

c)

$x=1$

d)

$x=-2$

23.

f\left(x\right)=5x^2-20x+1

Find the axis of symmetry

a)

x=2

b)

x=20

c)

x=-2

d)

x=10

24.

Label the Graph with the Correct Key Features.

1. (a) 2. (b)

3. (c) 4. (d)

Choose from the below words

Y-Intercept

Zero

Vertex

25.

Determine if the following quadratic equations have a maximum or minimum.

$x^2-2$ : (a)

$x^2+2x-3$ : (b)

$-x^2-2$ : (c)

Choose from the below words

Minimum

Maximum

26.

Whats the vertex of $f\left(x\right)=\left(x-2\right)^2-5$ (a)

Choose from the below words

(2,-5)

(2,5)

(-2,-5)

(-2,5)

27.

Identify the a, h, and k term from the following equation: $\left(x+3\right)^2+2$ (a)

Choose from the below words

a=-1, h=3, k=2

a=3, h=3, k=3

a=1, h=-3, k=2

a=1, h=-3, k=-2

28.

The graph of quadratic function f is shown on the grid.

Which of these best represents the domain of f?

a)

-3 ≤ x ≤ 2

b)

All real numbers

c)

y ≥ 5.5

d)

All real numbers less than -3 or greater than 2

29.

Which function is equivalent to $f\left(x\right)=-4\left(x+7\right)^2-6$

a)

$f\left(x\right)=-4x^2-56x-202$

b)

$f\left(x\right)=-4x^2+14x+43$

c)

$f\left(x\right)=-4x^2-56x-172$

d)

$f\left(x\right)=-4x^2+190$

30.

The graph of $f\left(x\right)=x^2$ was transformed to create the graph of $g\left(x\right)=\left(x-7.5\right)^2$ . Which of these describes this transformation?

a)

A horizontal shift to the right 7.5 units.

b)

A horizontal shift to the left 7.5 units.

c)

A vertical shift down 56.25 units.

d)

A vertical shift up 56.25 units.

31.

The graph represents a quadratic function.

Choose the correct answer for each blank to complete the statement.

The function has a (a) value of (b) .

Choose from the below words

minimum

-8

maximum

-4

3

32.

The graph of $f\left(x\right)=x^2$ was transformed to create the graph of $g\left(x\right)=2x^2-5$ . Which of the following statements are true?

Select TWO correct answers.

a)

The graph of h will be narrower than the graph of g.

b)

The graph of h will be wider than the graph of g.

c)

The vertex of the graph of h is 5 units to the right of the vertex of graph g.

d)

The vertex of the graph of h is 5 units below the vertex of graph g.

e)

The y-intercept of the graph of h is 5 units above the vertex of the graph g.

33.

A graph of a quadratic function is shown. What are the zeros of the function?

Select two answers.

A

B

C

D

E

34.

A quadratic functions is defined as:

$f\left(x\right)=\left(x-4\right)^2+3$

What is the equation of the parabola in standard form?

(a)

Choose from the below words

$f\left(x\right)=x^2-8x^2+19$

$f\left(x\right)=x^2-8x-13$

$f\left(x\right)=x^2-4x+19$

$f\left(x\right)=x^2-4x-13$

$f\left(x\right)=x^2+8x+19$

35.

A quadratic is defined as $y=\left(x+3\right)^2-6$

What is the equation for this function in standard form?

Your answer needs to be in the form of:

$y=ax^2+bx+c$

Enter your answer in the space provided.

36.

What is the product of the expression:

$\left(2x+5\right)\left(x-4\right)$ ?

Your answer should be in the form of:

$ax^2+bx+c$

37.

Convert to standard form

$y=3\left(x+6\right)^2-2$

38.

Convert to standard form

$y=2\left(x+5\right)^2-3$

Quadratic Functions Review

Total questions: 38

Worksheet time: 1hrs 2mins

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