Free Printable Quadratics Practice

Worksheets

Quadratics Practice

Total questions: 45

Worksheet time: 5hrs 44mins

Name

Class

Date

a standard form equation has _________________

an $x^2$

two sets of parentheses

parentheses and an exponent of 2

a factored form equation has _________________

an $x^2$

two sets of parentheses

parentheses and an exponent of 2

a vertex form equation has _________________

an $x^2$

two sets of parentheses

parentheses and an exponent of 2

a standard form equation tells us _______________

the y-intercept

the x-intercepts/zeros

the vertex

a factored form equation tells us _______________

the y-intercept

the x-intercepts/zeros

the vertex

a vertex form equation tells us _______________

the y-intercept

the x-intercepts/zeros

the vertex

the max or min of the graph is represented by the ______________

x-intercepts/zeros

vertex

y-intercept

the graph changes direction at the ______________

x-intercepts/zeros

vertex

y-intercept

if the equation starts with a negative, the graph will open _______

down

10.

identify the vertex.

11.

identify the y-intercept.

12.

identify both zeros/x-intercepts.

13.

identify the minimum.

14.

Does the following graph have a maximum or minimum.

Maximum

Minimum

15.

Does this parabola have a minimum or maximum and what is its value?

minimum: 2

maximum: 2

minimum: 5

maximum: 5

16.

What are the x- intercepts?

x= 0 and x= -4

x= 0 and x= 4

y= 0

x= 2

17.

Use the graph to determine the solutions.

-1 and -3

1 and -3

1 and 3

-1 and 3

18.

Given y = -3x²-7x+8, which direction will the graph open?

Down

Left

Right

19.

Does y = -4x² have a maximum or minimum value?

maximum

minimum

20.

Which best describes the vertex of a parabola?

Any point on the parabola.

A point on the x-axis.

The highest or lowest point of a parabola

A point on the y-axis.

21.

What does vertex represent in the situation?

The diver was 25 meters high at zero seconds.

The diver reached the water at 3.5 seconds.

The diver's maximum height was 30 meters at 1 second.

At 2 seconds diver's height was 25 meters.

22.

What does the y-intercept represent in the situation?

The diver was 25 meters high at zero seconds.

The diver reached the water at 3.5 seconds.

The diver's maximum height was 30 meters at 1 second.

At 2 seconds diver's height was 25 meters.

23.

What does the x-intercept represent in the situation?

The diver was 25 meters high at zero seconds.

The diver reached the water at 3.5 seconds.

The diver's maximum height was 30 meters at 1 second.

At 2 seconds diver's height was 25 meters.

24.

The standard form of a quadratic equation is

y = ax² + bx + c

y = (x + p)(x - p)

y = a(x - h)² + k

25.

What is the y-intercept?
f(x) = -2x² + 4x - 6

(0, 6)

(0, -6)

(6, 0)

(-6, 0)

26.

Does this graph have a maximum or a minimum value?

maximum

minimum

27.

Select BOTH zeros of this graph.

(-5,0)

(0,-5)

(-2,-9)

(1,0)

28.

Select the vertex of this graph.

(-5,0)

(0,-5)

(-2,-9)

(1,0)

29.

Select the y-intercept of this graph.

(-5,0)

(0,-5)

(-2,-9)

(1,0)

30.

$y=4x^2+2x+6$
If you graphed this equation, would your graph open upwards or downwards?

upwards

downwards

31.

What is the vertex of this graph?

(4,1)

(0,3)

(1,4)

(3,0)

32.

What is the y-intercept of this graph?

(4,1)

(0,3)

(1,4)

(3,0)

33.

The parabola f(x) = -x² + 4x + 4...

Opens downward

Opens upward

34.

The x-intercepts of the parabola are...

(-7, 0) and (1, 0)

(0, -7) and (0, 1)

(0, -7)

(-3, -16)

35.

The x-intercepts are also called the...

solutions

y-intercepts

vertex

maximum/minimum

36.

What causes the graph of y = x² to open downward?

multiply the x² by a fraction

multiply the x² by a decimal

multiply the x² by a negative number

multiply the x² by a number greater than 1

37.

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?

USE DESMOS TO GRAPH

2 ft

80 ft

144 ft

64 ft

38.

How fast would you reach the water if you jump of a cliff using the formula:

h(t) = -16t² + 8t + 24?

1.5

1/4

39.

The length of a rectangle is 4 cm more than its width.

The area of the rectangle is 96 sq. cm. Find its dimensions.

4 cm by 24 cm

6 cm by 16 cm

8 cm by 12 cm

10 cm by 14 cm

40.

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

41.

The length of a rectangle is 6 meters more than the width. The area is 72 square meters. Find the length and width.

Length = 6, Width = 12

Length = 18, Width = 4

Length = 12, Width = 6

Length = 4, Width = 6

42.

You jump off a 24 foot high cliff and your fall is modeled by the function:

h(t) = -16t² + 8t + 24

When would you reach 16 feet above the water?

8 seconds

1 second

1/2 second

1/4 second

43.

A diver is standing on a platform above the pool. He jumps form the platform with an initial upward velocity of 8 ft/s. Use the formula: h(t) = −16 t² + 8t + 24

How high is the platform?

.25 ft

24 ft

25 ft

8 ft

44.

The profit from selling local ballet tickets depends on the ticket price. Using past receipts, we find that the profit can be modeled by the function:

p= -15x² +600x +60

What is the maximum profit you can make from selling tickets?

$6060

$20

$600

$10,250

45.

Heather dropped a water balloon over the side of her school building from a height of 80 feet. The approximate height of the balloon at any point during its fall can be represented by the following quadratic equation:

h = -16t² + 80

About how long did it take for the balloon to hit the ground?

1.73 seconds

2.24 seconds

2.45 seconds

2.83 seconds

100 %

Quadratics Practice

Total questions: 45

Worksheet time: 5hrs 44mins

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