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Quadratics - Graphing - Printable Math Worksheets 9th Grade - Wayground

Quadratics - Graphing

Cynthia Keyes

Created by Cynthia Keyes

20 questions

9th Grade

Math

Updated Oct 2026

Quadratics - Graphing is a Grade 9 mathematics worksheet that helps students interpret and analyze quadratic functions in both graphical and equation form. Across 20 multiple-choice questions, students identify vertices, x-intercepts or zeros, axes of symmetry, and maximum or minimum values from parabolas and equations. They also connect vertex form and standard form by converting equations and using each form to determine key features of a quadratic graph. This worksheet gives students focused practice reading the effects of signs, coefficients, and values in quadratic equations, including recognizing whether a parabola opens upward or downward and locating its vertex. It is suitable for guided instruction, independent practice, review, or a quick assessment of graphing-quadratics skills. The free printable worksheet includes a complete answer key for efficient checking and feedback.

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Quadratics - Graphing

Total questions: 20

Name
Class
Date
1.
Which of the following is the correct equation for the given graph?
Which of the following is the correct equation for the given graph?
a)
f(x) = (x - 2)2 - 1
b)
f(x) = (x + 2)2 - 1
c)
f(x) = -(x + 2)2 - 1
d)
f(x) = -(x - 2)2 - 1
2.
What are the Zeroes for this graph?

What are the Zeroes for this graph?

a)

x= 0 and x= -4

b)

x= 0 and x= 4

c)

y= 0

d)

x= 2

3.

Given the equation for this parabola, does this parabola have a maximum or minimum value?

 y = −(x−4)2 − 3y\ =\ -\left(x-4\right)^2\ -\ 3  

a)

Maximum

b)

Minimum

4.
Which quadratic function is represented by the graph?
Which quadratic function is represented by the graph?
a)
y = 2(x - 4)2 + 5
b)
y = 2(x + 4)2 + 5
c)
y = -2(x - 4)2 + 5
d)
y = -2(x + 4)2 + 5
5.
What are the green dots called?
What are the green dots called?
a)
axis of symmetry
b)
vertex
c)
parabola
d)
roots or x-intercepts
6.
What is the green dot on the parabola called?

What is the green dot on the parabola called?

a)

maximum

b)

minimum

c)

roots

d)

zeros

7.
Does this parabola have a maximum or minimum?
Does this parabola have a maximum or minimum?
a)
Maximum
b)
Minimum
8.
Determine the vertex of the parabola:
y = 5x2 - 20x + 13
a)
(5, -7)
b)
(-2, -7)
c)
(2, -7)
d)
(-7, -2)
9.
The axis of symmetry line passes through which point?
a)
y-intercept
b)
any random point
c)
vertex
d)
none of these
10.
What are the x-intercepts (zeros)?

What are the x-intercepts (zeros)?

a)

x = -2 and x = 2

b)

x = -1 and x = 1

c)

x = 0

d)

x = 2 and x = -4

11.
What is the equation for the axis of symmetry?

What is the equation for the axis of symmetry?

a)

x = -1

b)

x = 8

c)

x = 1

d)

x = -3

12.


 y=4(x+2)2−8y=4(x+2)^2-8 

Convert the equation from vertex form to standard form. 

a)

 y=4x2+16x+8y=4x^2+16x+8  

b)

 y=4x2+16x+16y=4x^2+16x+16  

c)

 y=16x2+64x−8y=16x^2+64x-8  

d)

 y=16x2+256x+8y=16x^2+256x+8  

13.

Convert the equation from Standard Form to Vertex Form.

 y = 3x2+6x−5y\ =\ 3x^2+6x-5  

a)

y = 3(x + 1)2 - 8

b)

y = 3(x - 1) 2 - 8

c)

y = 3(x + 2)2 - 8

d)

y = 3(x - 2)2 - 8

14.

If given this equation, what is the vertex of the parabola?

 y = 3(x+5)2−4y\ =\ 3\left(x+5\right)^2-4  

a)

(5, -4)

b)

(-5, -4)

c)

(5, 4)

d)

(-5, 4)

15.

Given the following equation, does this parabola have a maximum or minimum value?

 y = −(x−4)2−3y\ =\ -\left(x-4\right)^2-3  

a)

Maximum

b)

Minimum

16.
What is the equation of this graph?

What is the equation of this graph?

a)

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

b)

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

c)

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

d)

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

17.
Identify the vertex and whether the graph opens up or down.
Identify the vertex and whether the graph opens up or down.
a)
(5, 2); opens up
b)
(5, 2); opens down
c)
(-5, 2); opens up
d)
(-5, 2); opens down
18.

Which equation has a vertex of (-3, 4)?

a)

y = 2(x+3)2 + 4

b)

y = (x + 3)2 - 4

c)

y = (x - 3)2 + 4

d)

y = 2(x - 3)2 + 4

19.
Which is the graph of the quadratic equation shown?

Which is the graph of the quadratic equation shown?

a)

A

b)

B

c)

C

d)

D

20.
Which is the graph the quadratic equation shown?

Which is the graph the quadratic equation shown?

a)

A

b)

B

c)

C

d)

D

WaygroundAnswer Key

Quadratics - Graphing

Total questions: 20

1.
b) f(x) = (x + 2)2 - 1
2.
b)

x= 0 and x= 4

3.
a)

Maximum

4.
d) y = -2(x + 4)2 + 5
5.
d) roots or x-intercepts
6.
a)

maximum

7.
b) Minimum
8.
c) (2, -7)
9.
c) vertex
10.
a)

x = -2 and x = 2

11.
a)

x = -1

12.
a)

 y=4x2+16x+8y=4x^2+16x+8  

13.
a)

y = 3(x + 1)2 - 8

14.
b)

(-5, -4)

15.
a)

Maximum

16.
b)

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

17.
c) (-5, 2); opens up
18.
a)

y = 2(x+3)2 + 4

19.
b)

B

20.
b)

B

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FAQs

What does the Quadratics - Graphing worksheet cover?

This Grade 9 worksheet uses 20 multiple-choice questions to practise reading quadratic graphs and equations. Students identify vertices, x-intercepts or zeros, axes of symmetry, and maximum or minimum values, then convert equations between vertex form and standard form. These tasks help students connect an equation’s structure to the key features of its parabola.

How can I use this worksheet to teach graphing quadratic functions?

Introduce the worksheet by reviewing how vertex form reveals the vertex and whether the parabola opens upward or downward, then connect those features to maximum or minimum values. Model one graph-to-equation question and one equation-conversion question before students work independently. Use the multiple-choice options to ask students to explain why a sign or coordinate makes one equation correct and the alternatives incorrect.

What mistakes should I watch for when students complete this quadratic graphing worksheet?

Watch for students reversing the sign of the x-coordinate in vertex form, such as reading x + 5 as a vertex coordinate of 5 instead of -5. Students may also confuse the vertex with the x-intercepts or axis of symmetry, or choose a maximum when the leading coefficient is positive and the parabola opens upward. During the conversion items, check that students expand the squared binomial and combine terms accurately.

How do I assign and grade this Quadratics - Graphing worksheet?

The worksheet is available as a printable PDF and as a digital quiz on Wayground, and it includes a complete answer key. You can grade printable submissions by scanning student work with the Wayground for Teachers app, while the digital quiz supports online response collection and scoring.

How can I differentiate this quadratic graphing worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing or font size so the graph-reading and equation questions are easier to navigate. You can also select a dyslexia-friendly font or translate the worksheet into another language when those options support access to the quadratic vocabulary and multiple-choice items.

Where can I find more worksheets like this on Wayground?

Wayground offers a comprehensive collection of free printable worksheets and practice problems across subjects, with downloadable PDFs and answer keys to support essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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