Free Printable All methods of solving quadratic equations

1.

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

a)

minimum: 2

b)

maximum: 2

c)

minimum: 5

d)

maximum: 5

2.

A parabola has a vertex at (-3,2).

What is the axis of symmetry?

a)

y = -2

b)

x = 3

c)

x = -3

d)

y = 2

3.

Use the picture to find the vertex and axis of symmetry

a)

Vertex (3,8) Axis x = 3

b)

Vertex (3,8) Axis y = 3

c)

Vertex (8,3) Axis x = 3

d)

Vertex (8,3) Axis y = 3

4.

What are the coordinates of the y-intercept?

a)

(-3, 0)

b)

(0, -3)

c)

(2, 1)

d)

y=-3

5.

What is another word for zeros?

a)

y-intercepts

b)

roots

c)

vertex

d)

axis of symmetry

6.

True or false:
The solutions, roots, x-intercepts, and zeros of a quadratic equation are all the same thing.

a)

True

b)

False, because the solution and root are the same but the x-intercept and zero are different

c)

False, because the x-intercept and root are the same but the zero and solution are different

d)

False, they are all different

7.

What is the first step to solving THIS equation by completing the square?
a² + 10a + 21 = 0

a)

Set the equation equal to zero

b)

Divide 10 by 2 and add the result to both sides

c)

Add a² and 10a together

d)

Subtract the 21

8.

Decide on the best method:
3a² + 13a = -4

a)

Square Root Method

b)

Factor Method

c)

Complete the Square

d)

Quadratic Formula

9.

Solve : b² - 2b - 8 = 0

a)

-2, 4

b)

-8

c)

±8

d)

No real solution

10.

What are the solutions of this graph?

a)

-2 and 3

b)

-1/2 and -6

c)

-2 and -6

d)

3 and -6

11.

Solve: 2n² + 4n - 16 = 0

a)

-4, 2

b)

-2, 4

c)

-16

d)

-4

12.

Solve the equation using the zero product property.

3x(2x - 4) = 0

a)

x = -1/3 or x = -2

b)

x = 0 or x = 2

c)

x = 0 or x = -2

d)

x = -1/3 or x = 2

13.

Use the graph to determine the solutions.

a)

-1 and -3

b)

1 and -3

c)

1 and 3

d)

-1 and 3

14.

What are the x- intercepts?

a)

x= 0 and x= -4

b)

x= 0 and x= 4

c)

y= 0

d)

x= 2

15.

What are the solutions of this graph?

a)

-2 and 3

b)

-1/2 and -6

c)

-2 and -6

d)

3 and -6

16.

Solve by finding square roots and simplify completely:
$x^2-16=0$

a)

$x=\pm16$

b)

$x=4$

c)

$x=\pm4$

d)

No real solutions

17.

Solve by finding square roots and simplify completely:
$x^2+20=0$

a)

$x=-20$

b)

$x=\pm2\sqrt{5}$

c)

$x=-2\sqrt{5}$

d)

No real solutions

18.

Solve
16a² - 9 = 0

a)

a = ^-3/₄, ³/₄

b)

a = ^-4/₃, ⁴/₃

c)

a = ^-9/₁₆, ⁹/₁₆

d)

a = ^-16/₉, ¹⁶/₉

19.

Solve by factoring:
$x^2-36=0$

a)

$x=\pm6$

b)

$x=\pm36$

c)

$x=\pm18$

d)

No real solutions

20.

Solve by factoring:
$x^2+2x-15=0$

a)

$x=3\ or\ x=-5$

b)

$x=\pm\sqrt{13}$

c)

$x=-3\ or\ x=5$

d)

No real solutions

21.

Solve by factoring:
$x^2-10x+16=0$

a)

$x=-2\ or\ x=-8$

b)

$x=\pm\sqrt{6}$

c)

$x=2\ or\ x=8$

d)

No real solutions

22.

Solve the following equation by completing the square:
n² - 2n - 3 = 0

a)

{3 and-1}

b)

{4 and -4}

c)

{5 and -3}

d)

{8 and -7}

23.

Solve by completing the square:
k² − 12k + 23 = 0

a)

{6 + √13, 6 - √13}

b)

{-6 + √13, -6 - √13}

c)

{6 + √59, 6 - √59}

d)

{-6 + √59, -6 - √59}

24.

Solve using the Quadratic Formula:
$x^2+10x+9=0$

a)

$x=1\ or\ x=9$

b)

$x=-1\ or\ x=-9$

c)

$x=-2\ or\ x=-18$

d)

No real solutions

25.

Use the quadratic formula to find the solutions for 2x² - 9x + 5 = 0

a)

-8.14 and 6.14

b)

-4.07 and 3.07

c)

$\frac{9\pm\sqrt[]{41}}{4}$

d)

ZERO solutions

26.

When does a quadratic equation have no real solutions?

a)

When you cannot factor it

b)

When it begins with a negative leading coefficient

c)

When there is a square root of a negative number

d)

When it only has two terms

27.

How many solutions does this graph have?

a)

one

b)

two

c)

no solutions

d)

cannot be determined

28.

What is another name for the x-intercepts and solutions of a quadratic?

a)

y-intercept

b)

Zeros

c)

x-axis

d)

They don't have another name

29.

Solve by using the best method (factoring, completing the square, or taking square roots):

x² + 4x= 12

a)

x = 2 and -2

b)

x = -6 and 2

c)

x = 6 and -2

d)

x = 1 and -1

30.

Solve by using the best method (factoring, completing the square, or taking square roots):

3x² - 36x = 39

a)

6 or -6

b)

13 or -1

c)

1 or -13

d)

36 or -39

31.

The height of a water balloon that is launched into the air is given by h(t) = -5x²+20x+25. When will the balloon explode on the ground?

a)

5 seconds

b)

1 second

c)

2 seconds

d)

3 seconds

32.

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?

a)

2 ft

b)

80 ft

c)

144 ft

d)

64 ft

33.

Rafael drops a ball from a third-story window. This equation represents the approximate height, h, in meters, of the ball above the ground after it falls for t seconds.
h = -5t² + 45
When is the ball at ground level?

a)

only at t = 0 seconds

b)

only at t = 3 seconds

c)

only at t = 9 seconds

d)

at both t = 0 seconds and t = 3 seconds

34.

A soccer ball is kicked from the ground with an initial upward velocity of 90 feet per second. The equation h=-16t²+ 90t gives the height h of the ball after t seconds.
How many seconds will it take the ball to hit the ground?

a)

126.56 ft

b)

5.625 sec

c)

2.81 sec

d)

0 ft

35.

You and some friends went to a haunted house on Halloween. The mummy scared one friend so much that she jumped into the air! The equation h = -4t² + 2t models her jump where h is her jump's height in feet t seconds after the mummy scares her. When did she reach her maximum height?

a)

0.1 seconds

b)

0.25 seconds

c)

0.50 seconds

d)

1 second

e)

2 seconds

All methods of solving quadratic equations

Total questions: 35

Worksheet time: 7hrs 40mins

Similar Resources on Wayground