Free Printable Ashley mathematics q.e

1.

Which is the standard form for a quadratic equation?

a)

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

b)

$ax^2+bx+c=0$

c)

$y=a\left(x-h\right)^2+k$

d)

$a^2+b^2=c^2$

2.

Which is in the proper factored form to use the Zero Product Property ?

a)

$x^2-x=12$

b)

$x\left(x-1\right)=12$

c)

$\left(x-4\right)\left(x+3\right)=1$

d)

$\left(x-4\right)\left(x+3\right)=0$

3.

Given this graph is the function of

y=x^2-2x-8

, what is the solution to

x^2=2x+8

?

a)

(1, 9)

b)

x = {-2, 4}

c)

(0, 8)

d)

x = {5, 2}

4.

$7x^2=6x-1$

Given this quadratic equation, what could be the values a, b, and c to use in the quadratic formula?

a)

$a\ =\ 7,\ b\ =\ -6,\ c\ =\ 1$

b)

$a\ =\ 1,\ b\ =\ 6,\ c\ =\ -7$

c)

$a\ =\ -7,\ b\ =\ 6,\ c\ =\ 1$

d)

$a\ =\ 6,\ b\ =\ 7,\ c\ =\ 1$

5.

$x^2+12x$

What value completes the square?

a)

3

b)

6

c)

12

d)

36

6.

$x^2-7x=0$

Solve by the method of your choice.

a)

x = 7 only

b)

x = 0 only

c)

x = 0 and 7

d)

There is no real answer for this equation.

7.

$3x^2-10x+1=0$

Solve by the method of your choice.

a)

$x=\frac{-10\pm\sqrt{88}}{6}$

b)

$x=\frac{-5\pm2\sqrt{22}}{3}$

c)

$x=\frac{10\pm\sqrt{112}}{6}$

d)

$x=\frac{5\pm\sqrt{22}}{3}$

8.

$2x^2=8x+3$

2x^2-8x-3=0

x=\frac{8\pm\sqrt{64-4\left(2\right)\left(-3\right)}}{4}

x=\frac{8\pm\sqrt{40}}{4}

x=\frac{8\pm2\sqrt{10}}{4}

x=\frac{4\pm\sqrt{10}}{2}

Suzanne solved the equation using this process.

Did she make a mistake?

If yes, at which line did she make her first mistake?

(There are 5 steps in her process)

a)

Suzanne made no errors.

b)

Step 2

c)

Step 3

d)

Step 4

e)

Step 5

9.

What is the color of the graph that has exactly one real zero?

a)

black

b)

green

c)

purple

d)

red

e)

None of these graphs has exactly one zero.

10.

What is the color of the graph that has no real zeros?

a)

black

b)

green

c)

purple

d)

red

e)

None of these graphs have no real zeros

11.

How many real solutions can a quadratic equation of the form shown have?
Check all that apply.

ax^2+bx+c=0

a)

0

b)

1

c)

2

d)

3

e)

infinitely many

12.

When using factoring to solve a quadratic equation, what must be true?

a)

The equation must be set equal to 1.

b)

The equation must be set equal to 10.

c)

The equation must be set equal to 0.

d)

It is not necessary to set the equation equal to anything.

13.

What is the correct simplification to

\sqrt{x^2}

? Check all that apply.

a)

1

b)

x

c)

| x |

d)

$\pm$ x

14.

What is/are the solution(s) to

3x^2-1=74

?

a)

x = 5 only

b)

x = -5 only

c)

x = 5 and -5

d)

There are no real solutions

15.

What should you do first in solving this equation?
x² + 6x - 13 = 3

a)

Get factored form

b)

Write down: a=1, b=6, c=-13

c)

Make it equal 0 by subtracting 3 on each side

d)

Type it all in a calculator.

16.

Solve by factoring: x² = 7x + 18

a)

-7 and -18

b)

9 and 2

c)

9 and -2

d)

2 and 7

17.

Solve for m by factoring.

a)

A

b)

B

c)

C

d)

D

18.

What is this formula?

a)

This is the speed of light formula.

b)

This is the quadratic formula.

c)

This is the zero product property.

d)

This is scary.

19.

Solve Using the Quadratic Formula
x² + 4x - 40 = -8

a)

-10 & -4

b)

-4 & 10

c)

-8 & 4

d)

8 & -4

20.

Solve the following for x by using the Quadratic Formula

2x²+6x=7

a)

b)

c)

21.

Solve by the Extraction of Roots method: x² = 16

a)

± 4

b)

± 8

c)

4

d)

8

22.

Solve by the Extraction of Roots method: -5x² = -50

a)

± 5

b)

± 10

c)

± √10

d)

-10

23.

Solve by the Extraction of Roots method: (x - 2) ² = 49

a)

9 or -5

b)

± 9

c)

± 5

d)

± 7

24.

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

25.

Find the missing value "c" to create a perfect square trinomial:
x² – 8x + ___

a)

-4

b)

16

c)

4

d)

8

26.

Complete the square for
x² + 12x + ____

a)

x² + 12x + 144

b)

x² + 12x + 36

c)

x² + 12x - 36

d)

x² + +12x - 144

27.

Complete the square.
x² + 14x + ____

a)

x² + 14x - 196

b)

x² + 14x + 49

c)

x² + 14x - 49

d)

x² + 14x + 196

28.

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

a)

4

b)

2

c)

8

d)

20

29.

Solve the following quadratics equation by completing the square...

x² + 4x + 1 = 0

a)

x = -2 ± √3

b)

x = -3 ± √2

c)

x = 2 ± √3

d)

x = 2 ± √2

30.

Solve the equation by completing the square and then finding the roots.
x²+ 6x - 4 = 36

a)

x = -7, 7

b)

x = 4, -10

c)

x = -4 +- √7

d)

x = 10, -4

31.

Solve by ANY method you have learned: x²−2x+11=0

a)

1±i√10

b)

1±√10

c)

-1±i√10

d)

-1±√10

32.

When will a quadratic equation have no solution?

a)

When it does not equal 0.

b)

When there is a negative in the square root.

c)

When there is a bx term.

d)

When there is no product/sum numbers.

33.

Which of the following cannot be solved with the Square Root method?

a)

x²-9=0

b)

x²-15=0

c)

x²-9x=0

d)

6x²-15=0

34.

What is the first step to solving x²-9x=10 with Factoring?

a)

Look for 2 numbers whose sum is -9 and product is 10.

b)

Subtract 10 from both sides.

c)

Divide -9 by 2 and square the answer.

d)

Look for 2 numbers whose sum is 10 and product is -9.

35.

When using the Quadratic Formula method, what are a, b, and c for the equation: 9x²-x+7=2?

a)

a=9, b = -1, c =7

b)

a=1, b = 0, c =7

c)

a=9, b = -1, c =5

d)

a=9, b = 7, c =2

36.

When using the Completing the Squares method, what number would fill in the blank:

x²+12x ______ = 8 + _______

a)

6

b)

36

c)

12

d)

16

37.

Using the Square Root method, what is the first step to solving the equation: 8x²+9=10

a)

Subtract 10 from both sides

b)

Divide by 8

c)

Subtract 9 from both sides

d)

Take the square root of both sides.

38.

When using the Quadratic Formula method, what are a, b, and c for the equation: 9x²-x= 0?

a)

a=9, b = -1, c =0

b)

a=1, b = 0, c =0

c)

a=9, b = 0, c =0

d)

a=9, b = 1, c =0

39.

Which method will work well for ANY quadratic equation?

a)

Factoring

b)

Square Root

c)

Completing the Sqare

d)

Quadratic Formula

40.

Other names for x-intercepts when talking about quadratic equations.

Check all that apply.

a)

zeros

b)

solutions

c)

x-intercepts

d)

roots

e)

answers

41.

What are the values for a, b, c? Type the number answers with a comma between.

4x^2-5x+10=0

(a)

42.

Which method would be best to solve the following quadratic equation?

\left(3x+5\right)^2=36

a)

square root

b)

complete the square

c)

quadratic formula

43.

Which method would be best to solve the following quadratic equation?

3x^2+5x=10

a)

square root

b)

complete the square

c)

quadratic formula

44.

Which method would be best to solve the following quadratic equation?

x^2+6x=25

a)

square root

b)

complete the square

c)

quadratic formula

45.

Solve

4x^2+2=22

a)

$\pm11$

b)

$\pm5$

c)

$\pm\sqrt{5}$

d)

11

46.

What is the value of c in this quadratic equation?

10x^2-8x=0

a)

10

b)

-8

c)

0

d)

2

47.

Solve

\left(x-5\right)^2=81

a)

86

b)

$\pm9$

c)

-14,4

d)

-4,14

48.

Solve

\left(4x-1\right)^2=7

a)

$\frac{\sqrt{7}\pm1}{4}$

b)

$\frac{-1\pm\sqrt{7}}{4}$

c)

$\frac{1\pm\sqrt{7}}{4}$

d)

$\frac{3}{2},4$

49.

Solve and select the BEST answer.

3x^2+1x+5=0

a)

$\frac{-1\pm\sqrt{59}}{6}$

b)

$\frac{1\pm\sqrt{59}}{6}$

c)

$\frac{-1\pm\sqrt{-59}}{6}$

d)

no real solutions

50.

Solve

x^2-4x-5=0

a)

-1,5

b)

-1,-4

c)

$\pm\sqrt{5}$

d)

-5,1

51.

$x^2-x-6=0$

Solve

a)

-2,3

b)

2,3

c)

-2,-3

d)

1,6

52.

Solve by completing the square.
x² + 4x= 12

a)

x = 2 and -2

b)

x = -6 and 2

c)

x = 6 and -2

d)

x = 1 and -1

53.

Determine the values of
a, b, and c for
the quadratic equation:
4x² – 8x = 3

a)

a = 4, b = -8, c = 3

b)

a = 4, b =-8, c =-3

c)

a = 4, b = 8, c = 3

d)

a = 4, b = 8, c = -3

54.

Solve using the Quadratic Formula:

2x² + 2x − 12 = 0

a)

x = −2, 3

b)

x = 2, 3

c)

x = 2, −3

d)

x = −2, −3

55.

Find the zeros of the quadratic equation y=4(x+9)²-36

a)

x=-9+√6 & x=-9-√6

b)

x=3 & x=-3

c)

x=-6 & x=-12

d)

so solution

56.

Solve the following for x by using the Quadratic Formula

2x²+6x=7

a)

b)

c)

57.

a)

±72

b)

±12

c)

12

d)

No real solution

58.

Solve
x² + 13x + 12 = 0

a)

x = -12, -1

b)

x = 12, 1

c)

x = 13, 1

d)

x = -13, -1

59.

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

a)

$x=\pm10$

b)

$x=\sqrt{10}$

c)

$x=\pm\sqrt{10}$

d)

No real solutions

60.

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

61.

Solve using the Quadratic Formula:
$5x^2+3x-1=0$

a)

$x=\frac{3\pm\sqrt{29}}{5}$

b)

$x=\frac{8}{5}\ or\ x=-\frac{2}{5}$

c)

$x=\frac{-3\pm\sqrt{29}}{10}$

d)

No real solutions

62.

Solve Using the method of your choice.

x² + 4x - 40 = -8

a)

-10 & -4

b)

-4 & 10

c)

-8 & 4

d)

8 & -4

63.

Solve the following quadratic equation:
Solve the following quadratic equation: $2x^2-5x+2=0$

a)

$x=\frac{-1}{2}$ & $x=-2$

b)

$x=-1$ & $x=-4$

c)

$x=4$ & $x=1$

d)

$x=\frac{1}{2}\ \&\ x=2$

64.

What are the roots of the quadratic equation

3x^2\ +\ 4x\ \ \ \ -\ 15\ =\ 0

?

a)

3, -5

b)

-3, 5

c)

3, $\frac{-5}{3}$

d)

-3, $\frac{5}{3}$

65.

Solve the quadratic equation by using the quadratic formula.

2x² -3x = -4

a)

b)

c)

d)

66.

$6x^2+12x+1=0$

Solve by using the quadratic formula.

a)

$\frac{-6\pm\sqrt{30}}{6}$

b)

$\frac{-6\pm\sqrt{30}}{12}$

c)

$\frac{-12\pm\sqrt{30}}{6}$

d)

$\frac{-6\pm\sqrt{42}}{6}$

67.

Use the graph to determine the solutions.

a)

-1 and -3

b)

1 and -3

c)

1 and 3

d)

-1 and 3

68.

Ben and Isaiah are solving the same problem who is correct?

a)

Ben

b)

Isaiah

c)

Both are correct

d)

neither one is correct

69.

Solve the following quadratic equation using the Quadratic Formula.

$5n^2+9n-38=0$

a)

n = 2 & n = $-\frac{19}{5}$

b)

$\pm\sqrt{2}$

c)

$\pm5$

d)

$\pm\frac{5}{2}$

70.

For the function below, is the discriminant positive, negative, or zero?

y = x² + 4x + 4

a)

Positive

b)

Negative

c)

Zero

71.

In the quadratic formula, if b²-4ac>0, then the quadratic equation has

a)

two imaginary solutions

b)

two different real solutions

c)

two equal real solutions

d)

none of these

72.

Which one refers to a polynomial equation in the form ax²+bx+c=0 where a, b, c are real numbers a≠0.

a)

Linear Equation

b)

Quadratic Equation

c)

Quadratic Polynomial

d)

Quadratic Inequalities

73.

Which of the following is NOT a quadratic equation?

a)

$𝟕+𝟑𝒅–𝒅^2=𝟎$

b)

$(𝒅–𝟓)(𝒅+𝟔)=𝟎$

c)

$𝟏𝟔=(𝒅−𝟓)^2$

d)

$𝟐(𝒅–𝟏𝟎)=𝟒𝒅$

74.

What must be added to x²+ 6x to make it a perfect square trinomial?

a)

3

b)

6

c)

9

d)

36

75.

Which of the following values of x make the equation x²– 5x – 36 = 0?

I. – 4

II. 9

III. – 6

a)

I and II

b)

II and III

c)

I and III

d)

III only

76.

One of the roots of 2x²+ 13x + 18= 0 is – 2. What is the other root?

a)

$–18$

b)

$-9$

c)

$-\frac{9}{2}$

d)

$-\frac{1}{2}$

77.

What number must be added to complete the square in the equation p² – 30p = 8?

a)

900

b)

225

c)

30

d)

15

78.

Which of the following is NOT a method in solving a quadratic equation?

a)

Factoring

b)

Quadratic Formula

c)

Completing the Square

d)

Discriminant

79.

The area of a rectangular lot is 56m². The length is six more than twice the width, if w represents the width, what expression will represent the length?

a)

56 – 2w

b)

2w + 6

c)

6 - 2w

d)

6w

80.

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

a)

$x=-1,\ x\ =\ 1$

b)

$x=-2,\ x\ =\ 8$

c)

$x=-4,\ x\ =\ 4$

d)

$x\ =\ -16,\ x\ =\ 16$

81.

Use the quadratic formula to solve 2x² + 2x - 12 = 0

a)

x = -2, x = 3

b)

x = 2, x = 3

c)

x = 2, x = -3

d)

x = -2, x = -3

82.

Solve by completing the square.
x² + 4x= 12

a)

x = 2 and -2

b)

x = -6 and 2

c)

x = 6 and -2

d)

x = 1 and -1

83.

ax²+bx+c=0 is the standard form of a quadratic equation.

a)

True

b)

False

84.

Determine the values of
a, b, and c for
the quadratic equation:
4x² – 8x = 3

a)

a = 4, b = -8, c = 3

b)

a = 4, b =-8, c =-3

c)

a = 4, b = 8, c = 3

d)

a = 4, b = 8, c = -3

85.

Solve the equation by factoring.
x² + 13x + 40 = 0

a)

-8, 5

b)

-40, -1

c)

5, 8

d)

-8, -5

86.

Which of the following does NOT illustrate quadratic equation?

a)

x² – 3x = 1

b)

2z(z² – 2z)=5

c)

y(y-2)=0

d)

5(m² - 3) + 4 = 0

Ashley mathematics q.e

Total questions: 86

Worksheet time: 2hrs 1mins

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