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Characteristics of Quadratics - Printable Mathematics Worksheets - Wayground

Characteristics of Quadratics

20 questions

9th - 9th Grade

Mathematics

This Grade 9 Algebra I worksheet helps students identify and interpret key characteristics of quadratic functions. Across 20 multiple-choice questions, students determine a parabola’s axis of symmetry, direction of opening, maximum or minimum, number of zeros, x-intercepts, domain, and range. They also connect quadratic vocabulary, including parabola, roots, vertex, and axis of symmetry, to equations and graphs. The worksheet is designed for guided practice, independent review, or a quick understanding check after instruction on quadratic functions. Several items require students to read information from an equation or vertex, while others assess whether they can recognize essential definitions and graph features. This free printable worksheet includes a complete answer key for efficient checking and feedback.

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Worksheets

Characteristics of Quadratics

Total questions: 20

Name
Class
Date
1.
What is the axis of symmetry for the following equation?
y=4x2-8x+9
a)
x=-8
b)
x=1
c)
x=-1
d)
x=2
2.
What direction is the following equation opening?
y=-3x2-7x+8
a)
Up
b)
Down
c)
Left
d)
Right
3.
Does
y = -4x2
have a maximum or minimum value?

a)
maximum
b)
minimum
4.
.How many zeros does this parabola have? 
a)
3
b)
2
c)
0
d)
1
5.
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
6.
Which answer choice describes  y = -3x2 +7x - 2 accurately?
a)
opens up with a maximum
b)
opens up with a minimum
c)
opens down with a maximum
d)
opens down with a minimum 
7.
Is this a max or min?
a)
max
b)
min
c)
cannot be determined
8.
What is the domain of the function?
a)
x≥3
b)
x≤3
c)
All real numbers
d)
-1≤x≤5
9.

What is the range of the function?

a)

y≤3

b)

y≥3

c)

All real numbers

d)

-6≤y≤3

10.
The graph of a quadratic function is called a
a)
Parabola
b)
Vertex
c)
Axis of Symmetry 
d)
Vertex Form
11.
What is another word for zeros?
a)
y-intercepts
b)
roots
c)
vertex
d)
axis of symmetry
12.
What are the x-intercepts?
a)
0 and 2
b)
-4 and 0
c)
2 and 3
d)
0 and 4
13.

What is the max/min value if the vertex is (2,-3)?

a)

Minimum of 3

b)

Minimum of -2

c)

Maximum of 0

d)

Maximum of 7

14.
What divides the parabola into 2 perfect halves?
a)
Axis of Symmetry
b)
Vertex
c)
Axis of Doom
d)
x - intercept
15.
The axis of symmetry is a line that goes through the...
a)
y-intercept
b)
any random point
c)
vertex
d)
 x-axis or y-axis
16.

What is the vertex?

a)

(1, -3)

b)

(-1, 3)

c)

(3, -1)

d)

(-3, 1)

17.

What is the axis of symmetry?

a)

x = -1

b)

x = -2

c)

y = -1

d)

y = -2

18.

What is the domain of the graph?

a)

-7 ≤ x < 5 , x∈R

b)

-3 ≤ x < 1 , x∈R

c)

-3 ≤ y < 1 , x∈R

d)

-7 ≤ y < 5 , x∈R

19.

What is the quadratic parent function?

a)

y = mx + b

b)

y = a(b)x

c)

y = x2

d)

Ax + By = C

20.

What is the vertex of this quadratic equation?

y = 2(x - 2)2 + 5

a)

(-2,5)

b)

(2,5)

c)

(5,-2)

d)

(-5,-2)

Answer Key

Characteristics of Quadratics

Total questions: 20

1.
b) x=1
2.
b) Down
3.
a) maximum
4.
b) 2
5.
c) x = -3
6.
c) opens down with a maximum
7.
a) max
8.
c) All real numbers
9.
a)

y≤3

10.
a) Parabola
11.
b) roots
12.
d) 0 and 4
13.
a)

Minimum of 3

14.
a) Axis of Symmetry
15.
c) vertex
16.
a)

(1, -3)

17.
b)

x = -2

18.
a)

-7 ≤ x < 5 , x∈R

19.
c)

y = x2

20.
b)

(2,5)

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FAQs

What does the Characteristics of Quadratics worksheet cover?

This Grade 9 Algebra I worksheet uses 20 multiple-choice questions to assess how students identify quadratic features, including the axis of symmetry, opening direction, maximum or minimum, zeros, x-intercepts, domain, and range. Students also apply vocabulary such as parabola, roots, and vertex to equations and graph descriptions, building fluency in interpreting quadratic functions.

How can I use this worksheet to teach characteristics of quadratics?

Introduce the worksheet by modeling how the leading coefficient indicates whether a parabola opens up or down, then connect that direction to its minimum or maximum. As students work through the multiple-choice items, ask them to justify axis-of-symmetry answers from the vertex and distinguish zeros or roots from other features such as the y-intercept and vertex.

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

Watch for sign errors when students determine whether an equation opens up or down, and for confusing the vertex’s x-coordinate with its y-coordinate when identifying the axis of symmetry. Students may also confuse roots with y-intercepts, select an incorrect range for an upward or downward parabola, or treat the domain as restricted instead of recognizing that a quadratic function has all real numbers as its domain.

How do I assign and grade this quadratics worksheet?

Wayground provides this worksheet as a printable PDF and as a digital quiz, with a complete answer key for checking all 20 multiple-choice questions. Printable submissions can be graded by scanning student work with the Wayground for Teachers app, while the digital quiz supports online completion and grading.

How can I differentiate this characteristics of quadratics worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing or increase the font size so equation-based multiple-choice items and answer choices are easier to read. You can also apply a dyslexia-friendly font or translate the worksheet into another language when those options better support access to the quadratic vocabulary and prompts.

Where can I find more worksheets like this on Wayground?

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

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