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Key Features of Quadratics - Printable Mathematics Worksheets class 10 - Wayground

Key Features of Quadratics

18 questions

9th - 12th Grade

Mathematics

Key Features of Quadratics is a free printable mathematics worksheet for students in Grades 9–12. It focuses on reading and interpreting quadratic graphs and functions by identifying vertices, x- and y-intercepts, roots or zeros, axes of symmetry, and maximum or minimum points. Students also evaluate functions and determine what specific ordered pairs represent on a graph. The 18-item worksheet uses a varied digital and printable format: 14 multiple-choice questions, one hotspot item, two classification items, and one drag-and-drop task. Several questions require students to select multiple zeros or choose the graph best supported by statements about its intercepts, zeros, and vertex. An answer key is included, making this worksheet useful for guided practice, independent review, or a quick assessment of students’ ability to connect quadratic features with coordinates and graph behavior.

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Key Features of Quadratics

Total questions: 18

Name
Class
Date
1.
Identify the vertex
a)
(-1,-9)
b)
(0,-8)
c)
(-4,0)
d)
(0,0)
2.

Which function has a maximum at (2, 0)?

a)
b)
c)
d)
3.

Which statement about the graph is FALSE?

a)

The vertex is (-3, 18)

b)

The vertex is a maximum

c)

The y-intercept is y = 0

d)

The axis of symmetry is y = -3

4.
Name the x-intercept(s)?
a)
(0, 0)
b)
(2, 4)
c)
(0, 0) and (0, 4)
d)
(0, 0) and (4, 0)
5.

What is the y-intercept of the quadratic function?

a)

2

b)

4

c)

-2

d)

0

6.

What is the significance of the ordered pair (0, -2) to the graph?

a)

It is the vertex

b)

It is an x-intercept

c)

It is the y-intercept

d)

It is the axis of symmetry

7.

What is the significance of the ordered pair (1, -2) to the graph?

a)

It is the maximum point

b)

It is the vertex

c)

It is the y-intercept

d)

It is an x-intercept

8.

Evaluate the function:

f(1)=f\left(1\right)=  

a)

0

b)

-2

c)

2

d)

4

9.

Evaluate the function:

f(3)=f\left(3\right)=  

a)

2

b)

1

c)

0

d)

-1

10.
Identify a root
a)
(-1,9)
b)
(0,-8)
c)
(-4,0)
d)
(0,0)
11.
Identify the y-intercept
a)
(-1,9)
b)
(0,-8)
c)
(-4,0)
d)
(0,0)
12.
Does this parabola have a maximum or minimum?
a)
Maximum
b)
Minimum
13.

The graph of a quadratic function is shown.

What are the zeros of the function?

(Select TWO correct answers)

A
B
C
D
E
F
14.

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

Find the graph that is best supported by ALL the statements below?

I. The coordinates of the y-intercept are (0, -6).

II. The graph has no zeros.

III. The graph has a maximum vertex.

a)

b)

c)

d)

15.

Which statements are best supported by the graph?

I. The graph has one zero

II. The coordinates of the y-intercept are (0, −1)\left(0,\ -1\right)

III. The axis of symmetry is x=−2x=-2

a)

I and II

b)

III only

c)

II and III

d)

I and III

16.

Organize these options into the right categories.

Categorize the following

The axis of symmetry is x = 1

The y-intercept is (0, -3)

The vertex is (-4, 1)

The minimum value is 1

Supported by the Graph
Not Supported by the Graph
17.

Organize these options into the right categories.

Categorize the following

The axis of symmetry is y = -2

The zeros are -5 and 1

The maximum value is 3

The y-intercept is (2, 0)

The vertex is (-2, 3)

Supported by the Graph
Not Supported by the Graph
18.

A graph of a quadratic function is shown. f(x)=−12x2+2x+4f\left(x\right)=-\frac{1}{2}x^2+2x+4

Move the correct answer to each box.

Not all answers will be used.​

(Keep Scrolling)

a. Identify the given characteristics of f(x).

y-intercept: ​ (a)  

Axis of symmetry: ​ (b)  

Choose from the below words
(0, 4)
x = 2
(4, 0)
x = -2
(2, 6)
(5, 0)
Answer Key

Key Features of Quadratics

Total questions: 18

1.
a) (-1,-9)
2.
c)
3.
d)

The axis of symmetry is y = -3

4.
d) (0, 0) and (4, 0)
5.
a)

2

6.
c)

It is the y-intercept

7.
b)

It is the vertex

8.
b)

-2

9.
c)

0

10.
c) (-4,0)
11.
b) (0,-8)
12.
b) Minimum
13.
14.
c)

15.
c)

II and III

16.
Supported by the Graph

The axis of symmetry is x = 1

The y-intercept is (0, -3)

Not Supported by the Graph

The vertex is (-4, 1)

The minimum value is 1

17.
Supported by the Graph

The zeros are -5 and 1

The maximum value is 3

The vertex is (-2, 3)

Not Supported by the Graph

The axis of symmetry is y = -2

The y-intercept is (2, 0)

18.
(0, 4), x = 2

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FAQs

What does the Key Features of Quadratics worksheet cover?

This worksheet helps students interpret quadratic functions and graphs by identifying the vertex, x- and y-intercepts, roots or zeros, axis of symmetry, and whether a parabola has a maximum or minimum. Its 18 questions combine multiple choice with hotspot, classification, and drag-and-drop tasks, requiring students to connect ordered pairs, graph features, and function values.

How can I use this worksheet to teach students the key features of quadratics?

Begin by having students annotate a sample parabola with its vertex, intercepts, zeros, and axis of symmetry, then use the worksheet’s multiple-choice items to check each feature individually. Ask students to explain why a coordinate represents a y-intercept, vertex, or root before moving to the hotspot and graph-selection questions, where they must use several features together as evidence.

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

Watch for students reversing x- and y-coordinates, confusing an x-intercept or zero with a y-intercept, or identifying a vertex without recognizing whether it is a maximum or minimum. In the hotspot item, students may select only one zero instead of both required zeros, while the graph-comparison questions may reveal difficulty using the vertex, intercepts, and zeros together to support a conclusion.

How do I assign and grade the Key Features of Quadratics worksheet?

Wayground provides this worksheet as both a printable PDF and a digital quiz, with a complete answer key for the 18 items. You can grade printable submissions by scanning student work with the Wayground for Teachers app, or review responses through the digital quiz.

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

In the worksheet’s Advanced Settings, adjust font spacing or font size to make the coordinate-based prompts and graph questions easier to navigate. You can also apply a dyslexia-friendly font or translate the worksheet into another language when those options better support students working through the multiple-choice, hotspot, classification, and drag-and-drop 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 help students master essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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