Key Features of a Parabola is a Grade 10 mathematics worksheet that helps students interpret the essential features of quadratic graphs and functions. Across 21 questions—20 multiple choice and 1 multiple select—students identify vertices, axes of symmetry, x- and y-intercepts, roots, and the coordinates of key points. They also connect the sign of a in a quadratic function to whether a parabola opens upward or downward and whether it has a minimum or maximum.
The worksheet reinforces mathematical vocabulary and representation skills by asking students to distinguish standard form from other forms, recognize the meaning of an x-intercept, and determine which functions match specified graph features. It is useful for guided practice, independent review, or a quick assessment of students’ ability to read parabola graphs and connect equations with their key features. This free printable worksheet includes a complete answer key for efficient checking.
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Key Features of a Parabola
Total questions: 21
Name
Class
Date
1.
Identify the vertex
a)
(-1,-9)
b)
(0,-8)
c)
(-4,0)
d)
(0,0)
2.
Name the Axis of Symmetry
a)
x = 1
b)
x = 0
3.
What is the axis of symmetry of the above graph?
a)
x = 3
b)
3
c)
y = -1
d)
-1
4.
What is the x value of the graph when the graph is at its max(or min)?
a)
-1
b)
3
c)
-0.5
d)
(3,-1)
5.
Which function has a maximum at (2, 0)?
a)
b)
c)
d)
6.
What are the roots of the function?
a)
3
b)
-6
c)
-1 and 3
d)
-6, -1, and 3
7.
What is the significance of the point (-3, 18)?
a)
x-intercept
b)
y-intercept
c)
vertex
d)
axis of symmetry
8.
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
9.
Which function has an x-intercept and y-intercept at (0, 0)?
a)
b)
c)
d)
10.
Name the x-intercept(s)?
a)
(0, 0)
b)
(2, 4)
c)
(0, 0) and (0, 4)
d)
(0, 0) and (4, 0)
11.
If "a" is negative, does the parabola open up or down? Does it have a maximum or minimum?
a)
Down, Max
b)
Down, Min
c)
Up, Max
d)
Up, Min
12.
Define X-intercept
a)
The highest or lowest point on the graph
b)
Where the parabola touches or intersects the x-axis
c)
Where the parabola touches or intersects the y-axis
d)
A line that divides the graph into two equal parts. i.e. cuts the graph in half
13.
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
14.
The axis of symmetry line passes through which point?
a)
y-intercept
b)
any random point
c)
vertex
d)
none of these
15.
What is the name of this form: y = ax2 + bx + c
a)
vertex form
b)
standard form
c)
factored form
d)
zero form
16.
What is the axis of symmetry? (hint: Graph it in calculator!)
f(x) = x2 - 8x + 15.
a)
x = -4
b)
x = 4
c)
y = 4
d)
y = -4
17.
What is the axis of symmetry? (hint: Graph it in calculator!)
y = 3x2 - 6x + 4
a)
x=1
b)
x=-6
c)
x=2
d)
x=-1
18.
Does the equation open up or down? Y = -3x2 +7x - 2
a)
up
b)
down
c)
Neither; it opens to the right.
d)
Neither; it opens to the left.
19.
What is the y-intercept of the equation y = 2x2+8x+3?
a)
(0,3)
b)
(3,0)
c)
(0,2)
d)
y=8
20.
Find the vertex (hint: Graph it in calculator!)
y = x2 - 2x - 5
a)
(-2, 10)
b)
(-1, 15)
c)
(1, -6)
d)
(1, -12)
21.
Is this point (the vertex) a max or min?
a)
max
b)
min
Answer Key
Key Features of a Parabola
Total questions: 21
1.
a) (-1,-9)
2.
b)
x = 0
3.
a)
x = 3
4.
b)
3
5.
c)
6.
c)
-1 and 3
7.
c)
vertex
8.
d)
The axis of symmetry is y = -3
9.
c)
10.
d) (0, 0) and (4, 0)
11.
a) Down, Max
12.
b)
Where the parabola touches or intersects the x-axis
13.
c)
It is the y-intercept
14.
c) vertex
15.
b) standard form
16.
b)
x = 4
17.
a)
x=1
18.
b) down
19.
a) (0,3)
20.
c)
(1, -6)
21.
a) max
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FAQs
What does the Key Features of a Parabola worksheet cover?
This Grade 10 worksheet uses 20 multiple-choice questions and 1 multiple-select question to practise identifying and interpreting parabola features, including the vertex, axis of symmetry, roots, x-intercepts, y-intercepts, and maximum or minimum values. Students also connect the sign of the coefficient a with the direction a parabola opens and identify y = ax² + bx + c as standard form.
How can I use this worksheet to teach students the key features of a parabola?
Use the questions to build a vocabulary-to-graph sequence: first review the vertex, intercepts, roots, and axis of symmetry, then discuss how the coefficient a determines whether the graph opens up or down. Ask students to explain why the axis of symmetry passes through the vertex and how an ordered pair such as (0, -2) identifies a y-intercept. Finish by having students justify their choices on the maximum, minimum, and false-statement items.
What mistakes should I watch for when students complete this parabola worksheet?
Watch for students confusing x-intercepts with y-intercepts, especially when reading ordered pairs such as (0, -2) or identifying points on the x-axis. Students may also select the vertex instead of the axis of symmetry, report the vertex coordinates when asked for only its x-value, or reverse the effect of a negative coefficient by saying the parabola opens up and has a minimum. On the false-statement and multiple-select items, check that students distinguish a point’s significance from the equation of a line.
How do I assign and grade this Key Features of a Parabola worksheet?
The worksheet is available as a printable PDF and as a digital quiz on Wayground, and it includes a complete answer key for all 21 questions. For printable submissions, you can scan students’ completed work with the Wayground for Teachers app to help grade responses.
How can I differentiate this parabola worksheet for my students?
In the worksheet’s Advanced Settings, adjust font spacing or font size to make the graph-feature questions and coordinate choices easier to read. You can also apply a dyslexia-friendly font or translate the worksheet into another language when students need additional reading support for terms such as vertex, intercept, and axis of symmetry.
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 mastery of essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.
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