Quiz about Solving Quadratic Equations Prep Work

Question 1

x2 - 25

Accepted Answer

( x + 5 ) ( x - 5 )

Answer

( x - 5 ) ( x - 5 )

Answer

( x + 5 ) ( x + 5 )

Answer

Unfactorable

Question 2

x4 - 16

Accepted Answer

( x² - 4) ( x² + 4)

Answer

( 2x - 4) ( 2x + 4)

Answer

( x² - 8) ( x² + 8)

Answer

( x - 4) ( x + 4)

Question 3

x2 - 225

Accepted Answer

( x - 15) ( x + 15)

Answer

( x + 15) ( x + 15)

Answer

Unfactorable

Answer

( x - 15) ( x - 15)

Question 4

Factor the Polynomial:

121r² - 64t²

Accepted Answer

(11r + 8t)(11r - 8t)

Answer

(11r - 8t)(11r - 8t)

Answer

(11r + 8t)(11r + 8t)

Answer

Unfactorable

Question 5

Fully Factor the Following
25x²-81

Accepted Answer

(5x+9)(5x-9)

Answer

(5x-9)2

Answer

25(x-9)2

Answer

(9x+5)(9x-5)

Question 6

Solve by factoring.

x² + 15x + 44 = 0

Accepted Answer

{-11, -4}

Answer

{-8, 2}

Answer

{-7, 5}

Answer

{-11}

Question 7

Convert the equation y= x²-2x-5 into vertex form.

Accepted Answer

y= (x-1)²-6

Answer

y= -(x-1)²-6

Answer

y= (x+1)²-6

Answer

y= -(x+6)²-1

Question 8

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

Accepted Answer

f(x) = (x + 6)² - 38

Answer

f(x) = (x + 6)² + 142

Answer

f(x) = (x + 6)² - 34

Answer

f(x) = (x + 6)² + 34

Question 9

Convert the equation y= x²+4x into vertex form.

Accepted Answer

y= (x+2)²-4

Answer

y= (x+4)²-4

Answer

y= (x-2)²+4

Answer

y= (x+2)2

Question 10

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

Accepted Answer

(-2, 16)

Answer

(2, 0)

Answer

(2, 4)

Answer

(-2, 4)

Question 11

Convert x²- 9x + 20 to factored form and solve.

Accepted Answer

(x-4)(x-5); x = 4, 5

Answer

(x-10)(x+2); x = -2, 10

Answer

(x+4)(x+5); x = -5, -4

Answer

Not factorable

Question 12

The solutions of the quadratic equation
x²+2x-15=0 are

Accepted Answer

x = -5 or x = 3

Answer

x = 3 or x = 5

Answer

x = 5 or x = -3

Answer

x = -3 or x = -5

Question 13

Factor x²+ 6x + 9 and solve for x.

Accepted Answer

(x+3)(x+3); x = -3

Answer

(x+4)(x+5); x=-4, -5

Answer

(x-3)(x-3); x=3

Answer

Not factorable

Question 14

What are the solutions to this equation? (x-3)(x+2)=0

Accepted Answer

x=3,-2

Answer

x=-3,2

Answer

x=2,3

Answer

x=3,2

Question 15

What is this formula?

Accepted Answer

This is the quadratic formula.

Answer

This is the standard formula.

Answer

This is the square root formula.

Answer

This is the Pythagorean formula

Question 16

Use the quadratic formula to find the solutions for

y = -x² - 5x + 12

Accepted Answer

Option B is correct

Answer

No Real Solution

Answer

C.

Answer

D.

Question 17

QUESTION 5

Accepted Answer

C

Answer

A

Answer

B

Answer

D

Question 18

How many x-intercepts can a quadratic have? Choose ALL THAT APPLY.

Accepted Answer

2

Accepted Answer

1

Accepted Answer

0

Answer

Cannot determine

Question 19

What is the y-intercept and what does it mean?

Accepted Answer

6; 6 feet is the height the ball is thrown from

Answer

(1.4, 31); At 1.4 seconds the football is at a maximum height of 31 ft

Answer

6; The ball lands at 6 seconds

Answer

31; The max height of the ball

Question 20

At what prices for a lemon slicer will this company make no money?

Accepted Answer

$10 and $50

Answer

$30

Answer

$10 and $60

Answer

$20 and $40

Question 21

About how long did it take for the football to reach its maximum height?

Accepted Answer

About 1.3 Seconds

Answer

About 3 seconds

Answer

About 0 seconds

Answer

About 2.6 Seconds

Question 22

About how long did it take the football to hit the ground?

Accepted Answer

About 2.6 Seconds

Answer

About 3 seconds

Answer

About 0 seconds

Answer

About 1.3 Seconds

Question 23

A goalie kicks a soccer ball upward. The quadratic function h(t) = -16t²+ 65t + 1 represents the height of the ball h in feet after t seconds. What is the maximum height of the ball?

Accepted Answer

y-value of the vertex

Answer

y-intercept

Answer

x-value of the vertex

Answer

Zeros/roots/solutions/x-intercepts of the function.

Question 24

A goalie kicks a soccer ball upward. The quadratic function h(t) = -16t²+ 65t + 1 represents the height of the ball h in feet after t seconds. How high off the ground did the goalie contact the ball to kick it?

Accepted Answer

y-intercept

Answer

x-value of the vertex

Answer

y-value of the vertex

Answer

Zeros/roots/solutions/x-intercepts of the function.

Question 25

A goalie kicks a soccer ball upward. The quadratic function h(t) = -16t²+ 65t + 1 represents the height of the ball h in feet after t seconds. How long will it take for the ball to hit the ground?

Accepted Answer

Zeros/roots/solutions/x-intercepts of the function.

Answer

y-intercept

Answer

x-value of the vertex

Answer

y-value of the vertex

Question 26

The height of a golf ball in the air can be modeled by the equation h(t) = -16t²+ 76t, where h(t) represents the height in feet after t seconds. When will the ball hit the ground?

Accepted Answer

Zeros/roots/solutions/x-intercepts of the function.

Answer

y-intercept

Answer

x-value of the vertex

Answer

y-value of the vertex

Question 27

The height of a golf ball in the air can be modeled by the equation h(t) = -16t²+ 76t, where h(t) represents the height in feet after t seconds. When will the ball reach it's maximum height?

Accepted Answer

x-value of the vertex

Answer

y-intercept

Answer

y-value of the vertex

Answer

Zeros/roots/solutions/x-intercepts of the function.

Question 28

The height of a golf ball in the air can be modeled by the equation h(t) = -16t²+ 76t, where h(t) represents the height in feet after t seconds. What is the ball's maximum height?

Accepted Answer

y-value of the vertex

Answer

y-intercept

Answer

x-value of the vertex

Answer

Zeros/roots/solutions/x-intercepts of the function.

Question 29

What do you do to the b value to correctly complete the square?

Accepted Answer

divide it by 2 and square the result

Answer

square it

Answer

divide it by 2 and take the square root of the result

Answer

divide it by 2 only

Question 30

When factoring
x² - 4x + 4 = 20,
what goes in the blank?
(x - __ )² = 20

Accepted Answer

2

Answer

4

Answer

8

Answer

20

Question 31

What is one of the solutions to this equation?
(2x - 1)² = 49

Accepted Answer

-3

Answer

7

Answer

-7

Answer

-4

Question 32

Complete the square.
x² + 6x + ____

Accepted Answer

x² + 6x + 9

Answer

x² + 6x - 36

Answer

x² + 6x + 36

Answer

x² + 6x - 9

Question 33

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

Accepted Answer

Zeros

Answer

y-intercept

Answer

x-axis

Answer

They don't have another name

Question 34

How many solutions does this graph have?

Accepted Answer

two

Answer

one

Answer

no solutions

Answer

all real numbers

Question 35

Find the x-intercepts of y=x².

Accepted Answer

(0,0)

Answer

(0,0)(1,0)

Answer

(-1,0)(1,0)

Answer

(-4,0)(4,0)

Question 36

Complete the square for

x² + 12x + ____

(find the missing number in the blank)

Accepted Answer

x² + 12x + 36

Answer

x² + 12x + 144

Answer

x² + 12x - 36

Answer

x² + +12x - 144

Question 37

Write the following quadratic expression in completed square form...

x² - 20x + 104

Accepted Answer

(x - 10)² + 4

Answer

(x + 10)² + 4

Answer

(x - 10)² - 4

Answer

(x + 10)² - 4

Question 38

Put the following function into vertex form.

f(x) = 3x²+9x-23

Accepted Answer

3(x + (3/₂))² - (¹¹⁹/₄)

Answer

(3x + (⁹/₂))²- (¹¹/₄)

Answer

3(x + 3)² - (²³/₃)

Answer

3(x + (³/₂))² - (¹¹⁹/₁₂)

Answer

3(x + (⁹/₄))² - (¹¹⁹/₄)

Question 39

When factoring

x² + 12x =13,

what goes in the blank?

(x + 6)² = __

Accepted Answer

49

Answer

18

Answer

13

Answer

36

Question 40

Solve by completing the square.
2x² + 12x = -10

Accepted Answer

-1 and -5

Answer

No Solution

Answer

-5

Answer

-1 and 5

Question 41

Convert the equation y= -3x²+24x-41 into vertex form.

Accepted Answer

y= -3(x-4)²+7

Answer

y= 4(x-3)²+7

Answer

y= -3(x+7)²+4

Answer

y= 3(x+4)²+7

Question 42

Convert
f(x) = -4(x - 1)² +7
to standard form.

Accepted Answer

f(x) = -4x² +8x + 3

Answer

f(x) = -4x² + 3

Answer

f(x) = -4x² - 8x + 17

Answer

f(x) = -4x² +8x - 11

Question 43

A frog is sitting on the ground when he is scared by a big dog. His movement is modeled by the equation h = -6t²+ 6t where h is the frog's height at any given time, t . How many seconds until the frog is back on the ground?

Accepted Answer

1 second

Answer

0.5 seconds

Answer

1.5 seconds

Answer

2 seconds

Answer

3 seconds

Question 44

A dolphin jumps from the water at at initial velocity of 16 feet per second. The equation h = -8t² + 16t models the dolphin's height at any given time, t. What is the maximum height the dolphin jumps?

Accepted Answer

8 feet

Answer

1 foot

Answer

5 feet

Answer

7 feet

Answer

12 feet

Question 45

A lizard is jumping across the water in search of food. The equation h = -12t² + 6t models the lizard's height in feet above the water t seconds after he jumps. How long after jumping is he back on the water?

Accepted Answer

0.50 seconds

Answer

0.1 seconds

Answer

0.25 seconds

Answer

0.75 seconds

Answer

1 second

Question 46

Your nephew is standing on his deck, which is 4 feet off the ground. He tosses his toy up into the air. The equation

h = -2t²+ 7t + 4 models the toy's height, h, from the ground at t seconds after he threw it. How high is the toy after 1 second?

Accepted Answer

9

Answer

2

Answer

4

Answer

10

Answer

15

Question 47

Amelia runs a catering business. Based on her records, her profit is shown by P = 2x² - 44x -150, where x is the number of meals she caters and P is her profit. When P is negative, Amelia loses money. What is the least number of meals Amelia needs to cater in order to begin making profit?

Accepted Answer

25

Answer

-1

Answer

5

Answer

11

Answer

50

Question 48

Your friend passes you the ball during a soccer game. The height off the ground is modeled by the equation

h = -4t² + 12t. How high did the soccer ball get?

Accepted Answer

9

Answer

1.5

Answer

3

Answer

5

Answer

15

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