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Factoring/Graphing Quadratics Unit Exam Review 4/27 - Printable Mathematics Worksheets - Wayground

Factoring/Graphing Quadratics Unit Exam Review 4/27

22 questions

9th - 9th Grade

Mathematics

Factoring/Graphing Quadratics Unit Exam Review 4/27 is a Grade 9 mathematics worksheet for reviewing how to interpret, transform, factor, and solve quadratic equations. Students identify vertices, axes of symmetry, roots or x-intercepts, opening direction, and equations represented by graphs, then apply factoring and the zero-product property to find solutions. The worksheet also includes questions about horizontal and vertical translations of the parent function y = x². With 22 items—21 multiple-choice questions and one drag-and-drop activity—this review checks both quadratic vocabulary and procedural understanding. Students must connect equations in vertex form and standard form to graph features, recognize how signs affect transformations, and select correct factorizations or roots. It is a free printable worksheet with an answer key, suitable for Grade 9 review, independent practice, or preparation for a unit assessment.

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Factoring/Graphing Quadratics Unit Exam Review 4/27

Total questions: 22

Name
Class
Date
1.

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)

2.

Which equation matches the graph?

a)

y=(x-2)2+3

b)

y=(x-2)2-3

c)

y=(x+2)2+3

d)

y=(x+2)2-3

3.
Where is the axis of symmetry for this parabola?
a)
x = −1
b)
x = 0
c)
y = 3
d)
x = −3
4.
What is the axis of symmetry?
y = 3x2 - 6x + 4
a)
x=1
b)
x=-6
c)
x=2
d)
x=-1
5.
What is the equation for axis of symmetry?
a)
y=3
b)
x=3
c)
x=5
d)
x=1
6.
What are the green dots called?
a)
axis of symmetry
b)
vertex
c)
parabola
d)
roots or x-intercepts
7.
The axis of symmetry line passes through which point?
a)
y-intercept
b)
any random point
c)
vertex
d)
none of these
8.
What are the x- intercepts?
a)
x= 0 and x= -4
b)
x= 0 and x= 4
c)
y= 0
d)
x= 2
9.
Factor
n2-13n+40
a)
(n-5)(n-8)
b)
(n+5)(n-8)
c)
(n-5)(n+8)
d)
(n+6)(n+1)
10.
How would you describe the translation from f(x)=x2  to  f(x)=(x-3)2 ?
a)
Horizontal translation: three units to the left
b)
Horizontal translation: three units to the right
c)
Vertical translation: three units up
d)
Vertical translation: three units down
11.
Shift f(x)=x2 three units to the left and 4 units down
a)
f(x)=(x+3)2-4
b)
f(x)=(x-3)2-4
c)
f(x)=(x+4)2-3
d)
f(x)=(x-4)2-3
12.
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.
13.

What is the "formula" for finding the axis of symmetry? 

a)

y=ax2+bx+cy=ax^2+bx+c  

b)

x=−b2ax=\frac{-b}{2a}  

c)

y=mx+by=mx+b  

d)

x=−b±b2−4ac2ax=\frac{-b\pm\sqrt{b^2-4ac}}{2a}  

14.
Solve for the values of x:
(x - 3)(x + 6) = 0
a)
{ -3, -6 }
b)
{ 3, -6 }
c)
{ -3, -6 }
d)
{ 3, 6 }
15.

x2 - 14x - 51 = 0

a)

x= 17 and -3

b)

x= -17 and 3

c)

x= -17 and -3

d)

x = 17 and 3

16.

Solve.

3x² + 5x = 12

a)

x = -4/3, x = 3

b)

x = 4/3, x = -3

c)

x = -1, x = 4

d)

x = 1, x = -4

17.

Find the solutions

a)

b=4/5, b=3

b)

b=4, b=-3

c)

b=1/5, b=3

d)

b=4/5, b=-3

18.

x2 - 16 = 0

a)

x = 4

b)

x = -4

c)

x = -4 and 4

d)

x = 16 and -16

19.

Factor out GCF first if necessary.

What is the factored form of:

2x2−2x−242x^2-2x-24

Move the correct answer to each box. Not all answers will be used.

​ (a)   (x+​ (b)   )(x-​ (c)   )

Choose from the below words
2
3
4
1
6
5
20.

The discriminant is

a)

aX2 + bX + c

b)

b - 4ac

c)

b2 - 4ac

d)

b2 + 4ac

21.

What is the discriminant of

-2x2 − x − 1 = 0 ?

a)

76

b)

-7

c)

9

d)

none of these

22.

For the function above, is the discriminant positive, negative, or zero?

a)

Positive

b)

Negative

c)

Zero

Answer Key

Factoring/Graphing Quadratics Unit Exam Review 4/27

Total questions: 22

1.
a)

(-2,5)

2.
a)

y=(x-2)2+3

3.
a) x = −1
4.
a) x=1
5.
b) x=3
6.
d) roots or x-intercepts
7.
c) vertex
8.
b) x= 0 and x= 4
9.
a) (n-5)(n-8)
10.
b) Horizontal translation: three units to the right
11.
a) f(x)=(x+3)2-4
12.
b) down
13.
b)

x=−b2ax=\frac{-b}{2a}  

14.
b) { 3, -6 }
15.
a)

x= 17 and -3

16.
b)

x = 4/3, x = -3

17.
d)

b=4/5, b=-3

18.
c)

x = -4 and 4

19.
2, 3, 4
20.
c)

b2 - 4ac

21.
b)

-7

22.
c)

Zero

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FAQs

What does this quadratic functions worksheet help Grade 9 students practice?

This worksheet reviews how to read and graph quadratic functions by identifying vertices, axes of symmetry, roots or x-intercepts, opening direction, and equations that match graphs. Its 21 multiple-choice questions and one drag-and-drop item also require students to factor quadratic expressions, solve factored equations, and write translations of y = x², connecting algebraic forms to graph features.

How can I use this worksheet to teach factoring and graphing quadratics?

Introduce the worksheet by modeling how the signs and coefficients in a quadratic equation reveal its vertex, axis of symmetry, opening direction, or translation. Then have students explain why a selected graph or factorization fits the equation, using the multiple-choice items for guided discussion before assigning the remaining review questions and drag-and-drop activity independently.

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

Watch for sign reversals when students identify a vertex or horizontal translation—for example, reading (x + 2)² as a shift right instead of left. Students may also confuse the axis of symmetry with an intercept, use a y-value instead of an x-value for roots, miss the negative sign in the axis-of-symmetry formula, or choose factors whose product and middle term do not match the quadratic.

How do I assign and grade this factoring and graphing quadratics worksheet?

On Wayground, you can assign this worksheet as a printable PDF or as a digital quiz, including its multiple-choice and drag-and-drop items. It includes a complete answer key, and printable submissions can be graded by scanning student work with the Wayground for Teachers app.

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

Use the worksheet’s Advanced Settings to adjust font spacing and font size so the equation-and-graph questions are easier to scan. You can also apply a dyslexia-friendly font or translate the worksheet into another language, depending on students’ reading needs.

Where can I find more free 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 support essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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