Free Printable U7 Review: Solving Quadratic Equations

1.

What constant do you need to add to complete the square?

y = x² - 12x + ?

a)

12

b)

36

c)

24

d)

-36

2.

(x - 10)² = 100

What is the most efficient first step to solving this equation?

a)

Distribute 2 into (x - 10)

b)

Add 10 on both sides.

c)

Square root both sides.

d)

Add 100 on both sides.

3.

How many solutions can quadratic equations have? Select all that apply.

a)

0

b)

1

c)

2

d)

3

4.

Another way to say the solution to an equation is...

Select all that apply.

a)

x-intercept(s)

b)

root(s)

c)

zero(s)

d)

y-intercept(s)

5.

If you had to complete the square, what is a valid first step?

x² + 10x + 11 = 5

Select all that apply.

a)

Add 25 on the left side.

b)

Minus 11 on both sides.

c)

Add 14 on both sides.

d)

Square root both sides.

6.

What should be the linear term that completes the square?

y = x² + ____ + 81

a)

9x

b)

18x

c)

-9x

d)

-18x

7.

Yuna is great at solving quadratic equations. Here is her work:

x² + 15x = -54

x² + 15x + 54 = 0

(x + 9)(x + 6) = 0

x = -9 and x = -6

How did she solve this equation?

a)

Completing the Square Method

b)

Factoring Method

c)

Quadratic Formula

d)

Guess and Check

8.

Yuna is great at solving quadratic equations. Here is her work:

x(x - 8) = 0

x = 0 and x = 8

How did she solve this equation?

a)

Zero Product Property

b)

Distributive Property

c)

Qudratic Formula

d)

Complete the Square

9.

What is the quadratic formula?

a)

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

b)

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

c)

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

d)

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

10.

Find the zeros using the zero product property.

-3(2 - x)(2x - 10) = 0

a)

x = {-2, 0, 5}

b)

x = {5, 6}

c)

x = {2, 5}

d)

The answer cannot be determined.

11.

x² - 9x + 8 = 0

Select the correctly factored equation.

a)

(x - 1)(x - 8) = 0

b)

(x + 1)(x + 8) = 0

c)

(x + 2)(x + 4) = 0

d)

(x - 2)(x - 4) = 0

12.

You are trying to solve a quadratic equation by the factoring method. What should you do after you factor?

a)

Apply zero product property.

b)

Use square root to both sides.

c)

Complete the square.

d)

Apply quadratic formula.

13.

What should you do FIRST before you apply the quadratic formula?

a)

Make sure the equation is in standard form = 0.

b)

Make sure a, b, and c are identified on the left side of the equation.

c)

Factor the equation = 0

d)

Distribute squared terms on both sides.

14.

x² - 36 = 0

This equation is called...

a)

Difference of Squares

b)

Perfect Square

c)

Factored Form

d)

This is not a quadratic equation.

15.

(-3x - 11)(-3x - 11) = 0

This equation is an example of...

a)

Perfect Square

b)

Difference of Squares

c)

This is not a quadratic equation.

d)

Vertex Form

16.

Use scrap paper:

Solve this equation by the factoring method.

x² - 11x + 22 = -2

a)

x = 8

x = 3

b)

x = 1

x = 24

c)

x = 4

x = 6

d)

x = 2

x = 12

17.

Use scrap paper:

Solve this equation using your preferred method.

4(x - 6)² - 27 = -23

a)

The solutions are rational.

b)

The solutions are irrational.

c)

The answer cannot be determined.

18.

Use scrap paper:

Solve this equation using your preferred method.

2(x + 5)² = 82

a)

Solutions are irrational.

b)

Solutions are rational.

c)

There are no solutions.

19.

You are trying to make a perfect square trinomial on the left side of the equation. What should you add to both sides?

x² - 8x = 19

a)

16

b)

64

c)

-19

d)

-16

20.

Given standard form ax² + bx + c = 0 with a = 1,

how can you determine the value of c?

a)

(b/2)²

b)

2b/2

c)

b²/2

d)

b/2²

21.

Rewrite the polynomial in standard form = 0

and then identify the value of b.

-8x² - x

a)

-1

b)

-8

c)

0

d)

There is no b.

22.

Rewrite the polynomial in standard form = 0 with a>1

and then identify the value of c.

4x² = 3x - 5

a)

-5

b)

5

c)

-3

d)

-4

23.

Use Scrap Paper:

Solve this equation by using the quadratic formula.

5x² - 30x + 20 = -x

Write the correct solution that's a whole number.

x = (a) (write only #)

24.

Use Scrap Paper:

Solve this equation by using the quadratic formula.

11x² - 12x + 4 = 6x²

Write the correct solution that's a fraction using backslash (example: 2/3)

x = (a) (write only #/#)

25.

Use Scrap Paper:

Solve this equation by using the quadratic formula.

20x² +13x + 2 = 0

The solution is -1/4 and (a) (write only #/#)

26.

Use Scrap Paper:

Solve this equation by using the quadratic formula.

5x² + 9x + 3 = 0

What should go under the square root?

$x\ =\ \frac{-9\pm\sqrt[]{???}}{10}$

a)

81

b)

21

c)

141

d)

-42

27.

Suppose we have a model for the height of a launched object (in meters), h, as a function of time t, defined by h(t) = -4.9t² + 28t + 2.1.

From what height was the object launched?

a)

4.9 meters

b)

28 meters

c)

2.1 meters

d)

You need to factor in the equation.

28.

Yuna is angry and throws her toys.

The height h(t) can be expressed as -16(x - 3)(x + 1) measured in inches.

When did the toy land?

a)

3 seconds later.

b)

1 second later.

c)

16 seconds later.

d)

Answer cannot be determined in factored form.

29.

Use Scrap Paper:

Solve the equation using your preferred method.

x² + 2x + 1 = 49

x = -8 and x = (a) (write only #)

30.

Use Scrap Paper:

Find the solutions by factoring method.

x² + 7x - 10 = -2x

Write the negative solution.

x = (a) (write only #)

31.

Is there a mistake? If yes, find the first mistake.

GIVEN: 2x² - 6 = 11x

Line #1: $x\ =\ \frac{-11\ \pm\sqrt[]{121\ +\ 48}}{4}$

Line #2: $x\ =\ \frac{-11\ \pm\sqrt[]{169}}{4}$

Line #3: $x\ =\ \frac{-11\ \pm13}{4}$

Line #4: $x\ =\ 0.5\ and\ x\ =\ -6$

a)

Line #1

b)

Line #2

c)

There is no mistake. It's correctly solved.

d)

Line #4

32.

Is there a mistake? If yes, find the first mistake.

GIVEN: 2x² - 6 = 11x

Line #1: $x\ =\ \frac{11\ \pm\sqrt[]{\left(-11\right)^2\ +\ 48}}{4}$

Line #2: $x\ =\ \frac{11\ \pm\sqrt[]{-121\ -169}}{4}$

Line #3: $x\ =\ \frac{11\ \pm\sqrt[]{-290}}{4}$

Line #4: $No\ Solution$

a)

Line #1

b)

Line #2

c)

Line #3

d)

No mistake!

33.

Identify the root(s).

a)

(-4, 0)

b)

(-1, 9)

c)

(0, 8)

d)

(2, 0)

34.

Identify the f(0).

a)

(-1, 0)

b)

(0, 6)

c)

(2.5, 12.25)

d)

(6, 0)

35.

True or False: Zero(s) of this graph is (0, 12).

a)

True.

b)

False.

U7 Review: Solving Quadratic Equations

Total questions: 35

Worksheet time: 3hrs 55mins

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