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Graphing Quadratics in Vertex Form - Printable Math Worksheets class 9 - Wayground

Graphing Quadratics in Vertex Form

Dominick Torro

Created by Dominick Torro

19 questions

9th Grade

Math

Updated Oct 2026

Graphing Quadratics in Vertex Form is a Grade 9 mathematics worksheet that helps students connect vertex-form equations with the features of their parabolas. Across 19 items—including a hotspot, four graphing tasks, multiple-choice questions, math responses, and a matching item—students identify vertices and axes of symmetry, interpret the roles of h and k, describe horizontal and vertical translations, match equations to graphs, and determine whether a graph has a maximum or minimum. The graphing items ask students to place a vertex and another point on each parabola, strengthening their ability to use vertex-form information to construct a graph rather than simply recognize one. Questions also reinforce how signs inside and outside the squared expression affect shifts and how the vertex represents the highest or lowest point. This free printable worksheet includes a complete answer key and is suitable for Grade 9 instruction, guided practice, independent review, or assessment.

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Graphing Quadratics in Vertex Form

Total questions: 19

Name
Class
Date
1.

Click on the dot where the vertex of the parabola is.

A
B
C
D
2.

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

You can drag one dot to the vertex and another to another point on the parabola.

3.

Graph y=−(x+1)2+3y=-\left(x+1\right)^2+3 .

You can drag one dot to the vertex and another to another point on the parabola.

4.

Graph y=(x+1)2+3y=\left(x+1\right)^2+3 .

You can drag one dot to the vertex and another to another point on the parabola.

5.

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

You can drag one dot to the vertex and another to another point on the parabola.

6.
A parabola has a vertex at (-3,2).
Where is the axis of symmetry?
a)
y = -2
b)
x = 3
c)
x = -3
d)
y = 2
7.
The equation of red graph is y = x 2 . What is the equation of the blue graph?

The equation of red graph is y = x2. What is the equation of the blue graph?

a)

y = (x + 5)2

b)

y = (x - 5)2

c)

y = x2 - 5

d)

y = x2 + 5

8.
What is the vertex of the graph?
What is the vertex of the graph?
a)
(-3,-2)
b)
(3,2)
c)
(2,3)
d)
(-2,-3)
9.
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
10.

Describe the horizontal shift for

y = 3(x + 4)2 - 1

a)

shifts 3 left

b)

shifts 4 left

c)

shifts 4 right

d)

shifts 1 left

11.
Which equation matches the graph?

Which equation matches the graph?

a)

f(x)=(x−1)2+4f\left(x\right)=\left(x-1\right)^2+4

b)

f(x)=(x+4)2−1f\left(x\right)=\left(x+4\right)^2-1

c)

f(x)=−(x−1)2+4f\left(x\right)=-\left(x-1\right)^2+4

d)

f(x)=−(x+4)2−1f\left(x\right)=-\left(x+4\right)^2-1

12.
In vertex form, what effect does the h have on the graph?

In vertex form, what effect does the h have on the graph?

a)

Translates Up/Down

b)

Translates Left/Right

c)

Narrows/Widens Parabola

d)

Flips it

13.
In vertex form, what effect does the k have on the graph?

In vertex form, what effect does the k have on the graph?

a)

Translates Up/Down

b)

Translates Left/Right

c)

Narrows/Widens Parabola

d)

Flips it

14.
Does this graph have a maximum or minimum?
Does this graph have a maximum or minimum?
a)
Minimum
b)
Maximum
15.
A minimum is the ______________ point of the function.
A minimum is the ______________ point of the function. 
a)
highest
b)
lowest 
16.

Write the equation of a parabola that opens downward and has a vertex of (2, 4)

17.

Write the equation of a parabola that opens upward and has a vertex of (-2, 3)

18.

The domain of a parabola is...

a)

All real numbers

b)

x>0

c)

x<0

d)

No Solution

19.

Match the following.

Vertex

The turning point of the parabola

Axis of Symmetry

The line that cuts the parabola in half

Domain

All possible input (x) values

Range

All possible output (y) values

Parabola

The shape of a quadratic graph

WaygroundAnswer Key

Graphing Quadratics in Vertex Form

Total questions: 19

1.
2.
3.
4.
5.
6.
c) x = -3
7.
d)

y = x2 + 5

8.
a) (-3,-2)
9.
a) y = 2(x+3)2 + 4
10.
b)

shifts 4 left

11.
a)

f(x)=(x−1)2+4f\left(x\right)=\left(x-1\right)^2+4

12.
b)

Translates Left/Right

13.
a)

Translates Up/Down

14.
a) Minimum
15.
b) lowest 
16.

y=−(x−2)2+4y=-\left(x-2\right)^2+4

17.

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

18.
a)

All real numbers

19.

Vertex

 - 

The turning point of the parabola

, 

Axis of Symmetry

 - 

The line that cuts the parabola in half

, 

Domain

 - 

All possible input (x) values

, 

Range

 - 

All possible output (y) values

, 

Parabola

 - 

The shape of a quadratic graph

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FAQs

What does the Graphing Quadratics in Vertex Form worksheet cover?

This Grade 9 worksheet focuses on reading and graphing quadratics in vertex form. Students identify vertices and axes of symmetry, interpret h and k as horizontal and vertical translations, match equations to graphs, determine maximum or minimum values, and graph four parabolas by placing the vertex and another point.

How can I use this worksheet to teach graphing quadratics in vertex form?

Begin by reviewing the form y = a(x − h)² + k and have students locate the vertex (h, k), then discuss how h controls the left-right shift and k controls the up-down shift. Use the four graphing items to model placing the vertex first and selecting a second point, then use the equation-and-graph questions to ask students to justify each shift and whether the parabola opens toward a maximum or minimum.

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

Watch for students reversing the sign of h, such as reading x + 4 as a shift right instead of 4 units left, or confusing h with k when identifying horizontal and vertical translations. Students may also place the vertex correctly but choose an incorrect second point, confuse the axis of symmetry with a horizontal line, or label a lowest point as a maximum rather than a minimum.

How do I assign and grade this worksheet?

The Graphing Quadratics in Vertex Form worksheet is available as a printable PDF and as a digital quiz on Wayground. It includes a complete answer key, and printable submissions can be graded by scanning student work with the Wayground for Teachers app. The printable format can also support schools that are reducing screen time.

How can I differentiate this worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing or increase the font size so the equation choices, graphing directions, and coordinate-based items are easier to read. You can also apply a dyslexia-friendly font or translate the worksheet into another language while keeping the vertex-form graphing tasks intact.

Where can I find more worksheets like this on Wayground?

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

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