Free Printable Quadratic Review

Worksheets

Quadratic Review

Total questions: 45

Worksheet time: 2hrs 39mins

Name

Class

Date

Match the description to its equation.
Reflected over the x-axis
Stretched by a factor of 2

Match the description to its equation.
Moves up 2
Moves left 4

Match the description to its equation.
Moves right 7

If the blue is f(x)=x^2,then the red must be

g(x)=x²-5

g(x)=x²+5

g(x)=(x-5)²

g(x)=(x+5)²

If the blue is f(x)=x^2,the red must be

g(x)=(x+3)²

g(x)=(x-3)²

g(x)=x²+3

g(x)=x²-2

Which of the following is the correct equation for the given graph?

f(x) = (x - 2)² - 1

f(x) = (x + 2)² - 1

f(x) = -(x + 2)² - 1

f(x) = -(x - 2)² - 1

Which quadratic function is represented by the graph?

y = 2(x - 4)² + 5

y = 2(x + 4)² + 5

y = -2(x - 4)² + 5

y = -2(x + 4)² + 5

If red represents y = x², which equation represents black?

y = 7x²

y = -7x²

y = -(1/7)x²

y = -5x²

Does this graph have a maximum or minimum value?

maximum

minimum

neither

both

10.

Which is the parent function of a parabola?

y = x²

y = 2x² + 3

y = -x² -4

y = -x²

11.

If given the equation y = 3(x + 5)² - 4, what is the vertex of the parabola?

(5, -4)

(-5, -4)

(-15, -4)

(15, -4)

12.

If the blue is f(x)=x^2,then the red must be

g(x)=x²-5

g(x)=x²+5

g(x)=(x-5)²

g(x)=(x+5)²

13.

Use transformations to identify the equation of the graph shown.

f(x) = (x + 3)² - 8

f(x) = 3(x + 3)² - 8

f(x) = (x - 3)² - 8

f(x) = 2(x - 3)² - 8

14.

If the blue graph is f(x) (the original function) and the red graph is the transformation, what is the equation of the red graph?

-f(x)

f(-x)

f^-1(x)

f(2x)

15.

Describe the transformations that maps
y = g(x) to y = - g(x + 6) - 10

Reflect over y-axis
Shifted down 10 units
Shifted left 6 units

Reflect over x-axis
Shifted up 10 units
Shifted left 6 units

Reflect over y-axis
Shifted up 10 units
Shifted right 6 units

Reflect over x-axis
Shifted down 10 units
Shifted left 6 units

16.

Which of the following equations matches standard form of a quadratic?

ax + by = c

y = a(x - h)² + k

y = ax² + bx + c

y = mx + b

17.

Which of the following shows
f(x) = x² + 12x - 2
written in vertex form?

f(x) = (x + 6)² + 142

f(x) = (x + 6)² - 34

f(x) = (x + 6)² - 38

f(x) = (x + 6)² + 34

18.

If given the equation y = 3(x + 5)² - 4, what is the vertex of the parabola?

(5, -4)

(-5, -4)

(-15, -4)

(15, -4)

19.

Which of the following forms are best to use if we want to identify the vertex of a quadratic equation?

Standard Form

Vertex Form

Intercept Form

20.

The graph of a quadratic function is called a

Parabola

Vertex

Axis of Symmetry

Vertex Form

21.

The axis of symmetry line passes through which point?

y-intercept

any random point

vertex

symmetrical point for the vertex

22.

Determine the vertex of the parabola y=5(x-2)²–7

(5, -7)

(-2, -7)

(2, -7)

(-7, -2)

23.

What is the axis of symmetry?
f(x) = x²- 8x + 15.

x = -4

x = 4

y = 4

y = -4

24.

Identify A, B, and C if y=3x²-8+5x

A=3, B=5, C=-8

A=3, B=-8, C=5

A=3x², B=5x, C=-8

A=3x² , B=-8, C=5x

25.

Find the axis of symmetry for
f(x) = x²- 8x + 15.

x = -4

x = 4

y = 4

y = -4

26.

What is the y-intercept of the following funtion
f(x) = -2x² +3x - 7

(0, -2)

(0, 3)

(0, -7)

(0, 7)

27.

Does the equation open or or down?
Y = -3x² +7x - 2

down

28.

The graph of y=-2x²+3 will have a:

minimum

maximum

neither

29.

Which value tells you the y-intercept?

30.

Which graph represents y=-x²+4

31.

If you know the axis of symmetry is x=2, select all the possible equations:

y=x²-4x+3

y=2x²+x-4

y=-2x²+8x

y=3x²-6x+5

32.

Find the vertex of the quadratic:
y = -2x² + 4x + 3

(0, 3)

(-1, 5)

(1, 5)

(1, -5)

33.

Determine the vertex of the parabola:
y = 5x²- 20x + 13

(5, -7)

(-2, -7)

(2, -7)

(-7, -2)

34.

What are the solutions to the system:
y = x² + 3x - 5
y = x + 3

(-4, 2) and (-1, 5)

(-4, -1) and (2, 5)

(2, -1 and (-4, 5)

(-4, 1) and (2, -1)

35.

Determine the solution to the given linear-quadratic function.

(0, 0)

(3, 0)

(2, -3)

(-3, 2)

36.

Determine the number of solutions to the given linear-quadratic system.

0 solutions

1 solution

2 solutions

3 solutions

37.

How many solutions does this system of equations have?

one solution

two solutions

no solution

infinitely many solutions

38.

If I want to find out when an object hits the ground, I should _________.

Use x = (-b/2a) as my answer.

Set my equation = 0 and solve.

Replace x with 0 and evaluate.

Find the y-coordinate of the vertex.

39.

When I want to find the maximum or minimum height of an object, I should_____.

Set the equation = 0 and solve.

Use x = (-b/2a) as my answer.

Substitute x = 0 into the equation.

Find the y-coordinate for the vertex.

40.

If I want to see the initial height of an object, I should _____________.

Substitute x = 0 into the equation and evaluate.

Use x = (-b /2a) as my answer.

Find the y-coordinate of the vertex.

Set my equation = 0 and solve.

41.

The length of a rectangular garden is 10 yards more than its width. If the area of the garden is 600 square yards, find the length & width of the garden.

The length is 30 & the width is 20

The length is 20 & the width is -30

The length is 60 & the width is 10

The length is 24 & the width is 25

42.

An object in launched directly upward at 64 feet per second (ft/s) from a platform 80 feet high. Its height is represented by the equation
s(t) = –16t² + 64t + 80.
What will be the object's maximum height?

2 ft

80 ft

144 ft

64 ft

43.

The function f(t) = -5t²+20t + 60 models the approximate height of an object t seconds after it is launched. How many seconds does it take the object to hit the ground?

4 seconds

-2 seconds

6 seconds

9 seconds

44.

i^6

-1

-i

45.

Use quadratic formula to solve: $8x^2-4x-18=0$

$\left\{\frac{1\pm\sqrt{37}}{4}\right\}$

$\left\{8,4,18\right\}$

$-\frac{5}{2}$

$i\sqrt{37}$

100 %

Quadratic Review

Total questions: 45

Worksheet time: 2hrs 39mins

Similar Resources on Wayground