Free Printable Quadratics

1.

Solve by factoring.
2x²-x -3=0

a)

x=-3/2 x=1

b)

x= 3/2 x= -1

c)

x= -3/2 x= -1

d)

x= 3/2 x= 1

2.

Solve by factoring.
3x² - 192 = 0

a)

-32 or 32

b)

No Solution

c)

-8 or 8

d)

-64 or 64

3.

What are the x- intercepts?

a)

x= 0 and x= -4

b)

x= 0 and x= 4

c)

y= 0

d)

x= 2

4.

Does the following quadratic equation have a maximum or minimum value? How can you tell?
y=x²+2x-3

a)

Minimum value, because the a value is positive

b)

Maximum value, because the b value is positive

c)

Maximum value, because the a value is positive

d)

Minimum value, because the c value is negative

5.

How many roots does this graph have?

a)

none

b)

1

c)

2

d)

infinite

6.

The x-intercepts of a quadratic equation are also known as the _____.

a)

Vertices

b)

Roots

c)

Squares

d)

Formulas

7.

The x-intercepts of a quadratic equation are also known as the _____.

a)

vertices

b)

squares

c)

zeros

d)

formulas

8.

What is the axis of symmetry y=4x²+8x+8?

a)

x = -1

b)

x = 1

c)

x = 2

d)

x = -2

9.

Solve by factoring.
3z² - 12z + 9 = 0

a)

z = 3 or z = -3

b)

z = 3

c)

z = 1 or z = 3

d)

z = 1 or z = -3

10.

Solve by factoring.
c² - 4c = 0

a)

c = 0 or c = -4

b)

c = 0 or c = 2

c)

c = 0 or c = 4

d)

c = 1 or c = -2

11.

Which equation below is a quadratic?

a)

y=9x+5

b)

y=(3n+2)(n-6)

c)

y=3x(5x²+6)

d)

x=3^x

12.

Find the vertex of
f(x) = -x²- 4x + 12.

a)

(-2, 16)

b)

(2, 0)

c)

(2, 4)

d)

(-2, 4)

13.

What is the equation for axis of symmetry?

a)

y=3

b)

x=3

c)

x=5

d)

x=1

14.

When a parabola opens downward the vertex is

a)

a minimum

b)

a maximum

c)

a vertex

d)

a parabola

15.

Solve.
(9x+1)(x-4)=0

a)

x=9 and 4

b)

x=1/9 and -4

c)

x=-1/9 and -4

d)

x=-1/9 and 4

16.

Which equation matches these solutions? x=5,-7

a)

(x+5)(x-7)=0

b)

(x-5)(x+7)=0

c)

(x+5)(x+7)=0

d)

(x-5)(x-7)=0

17.

What property would you use to solve the following?
(x-3)(x+2)=0

a)

Commutative Property

b)

Associative Property

c)

Zero Product Property

d)

Inverse Property

18.

Determine the line of symmetry.
y = x²+16x+64

a)

x=4

b)

x=2

c)

x=-8

d)

x=64

19.

Solve
2x²+7x-15=0

a)

-1.5 or 5

b)

No Solution

c)

-5 or 1.5

d)

0.7 or 5

20.

A rectangle has an area of 24 square meters. The width is 5 meters less than the length. What is the length, in meters, of the rectangle?

a)

6 m

b)

8 m

c)

3 m

d)

19 m

21.

Suppose you have 54 feet of fencing to enclose a rectangular dog pen. The function
A = 27x − x ², where x = width
gives you the area of the dog pen in square feet. What width gives you the maximum area? What is the maximum area? Round to the nearest tenth as necessary.

a)

width = 27 ft
area = 182.3 ft²

b)

width = 27 ft
area = 391.5 ft²

c)

width = 13.5 ft
area = 546.8 ft²

d)

width = 13.5 ft
area = 182.3 ft²

22.

The area of a playground is 336 yd². The width of the playground is 5 yards longer than its length. Find the length and width of the playground.

a)

length = 28 yd
width = 12 yd

b)

length = 12 yd
width = 28 yd

c)

length = 21 yd
width = 16 yd

d)

length = 16 yd
width = 21 yd

23.

Suppose that the equation
V = 20.8x² – 458.3x + 3,500
represents the value of a car from 1964 to 2002, where x represents the number of years after 1964. In what year did the car have the least value?

a)

1965

b)

1970

c)

1975

d)

1980

24.

What is the smallest of 3 consecutive positive integers if the product of the smaller two integers is 5 less than 5 times the largest integer?

a)

10

b)

-5

c)

5

d)

-10

25.

An object is launched directly upward at 64 feet per second (ft/s) from a platform that is 80 feet high.
What will be the object's maximum height?

a)

2 ft

b)

80 ft

c)

144 ft

d)

64 ft

26.

The product of two consecutive odd integers is 77 more than twice the larger. Which equation can be used to find the integers?

a)

(x)(x+2) = 2(x+2) + 77

b)

(x+1)(x+3) = 77+2 (x+1)

c)

x(x+1) = 2(x+1) + 77

d)

x + (x+2) = 2(x+2) + 77

27.

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

a)

(6 , 0)

b)

(-6 , 0)

c)

(0, -6)

d)

(0 , 6)

28.

The equation h = -16t² + 32t models the height of a ball. Without a calculator, determine how many seconds it takes for the ball to reach its highest point.

a)

-2 seconds

b)

2 seconds

c)

0 seconds

d)

1 second

29.

The curve of the main suspension cables on a suspension bridge can be modeled by the function y=0.04x² -x + 80 where y represents the height of the cable above the bridge surface and x represents distance along the bridge surface from one tower toward the other. How high are the towers?

a)

50 ft.

b)

80 ft.

c)

25 ft.

d)

Cannot be determined.

30.

The curve of the main suspension cables on a suspension bridge can be modeled by the function y=0.04x² -x + 80 where y represents the height of the cable above the bridge surface and x represents distance along the bridge surface from one tower toward the other. How far along the bridge does the cable reach the closest point to the bridge?

a)

12.5 ft.

b)

73.75 ft.

c)

25 ft.

d)

Cannot be determined.

31.

The curve of the main suspension cables on a suspension bridge can be modeled by the function y=0.04x² -x + 80 where y represents the height of the cable above the bridge surface and x represents distance along the bridge surface from one tower toward the other. What is the closest the cable comes to the bridge surface?

a)

12.5 ft.

b)

73.75 ft.

c)

25 ft.

d)

Cannot be determined.

32.

A cannon is shot into the air and follows the path h(t)=-12t²+168t. What are the TWO times when the cannon will be 156 ft above the ground?

a)

1 sec and 13 sec

b)

1.5 sec and 4 sec

c)

0 sec and 14 sec

d)

3 sec and 7 sec

33.

What equation could model the height above the ground, in ft, t seconds after an object is dropped from 50 feet above the ground?

a)

h(t) = 50t² - 16

b)

h(t) = -16t² + 50t

c)

h(t) = 50 - 16t²

d)

h(t) = -50 + 16t²

Quadratics

Total questions: 33

Worksheet time: 1hrs 7mins

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