Free Printable Solving Quadratics by Factoring and Quadratic Formula

Worksheets

Solving Quadratics by Factoring and Quadratic Formula

Total questions: 25

Worksheet time: 6hrs 15mins

Name

Class

Date

Solve for X:

(x-5)(x+6)=0

{5,5 }

{ -5,-5 }

{ -5,-6 }

{5,-6 }

What is the first step in solving
(x + 2)(x - 3) = 0 ?

Plug in zero for x

Solve for x

FOIL

Set each binomial factor equal to zero

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

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

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

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

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

Solve the quadratic equation.

-2, 4

-8

±8

No real solution

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

-2, 3

2, 3

2, -3

-2, -3

Solve the quadratic equation.

-4, 2

-2, 4

-16

-4

Convert x²+6x+9=0 to factored form and identify the solution.

(x+3)(x+3)=0; x=-3

(x+4)(x+5)=0; x=-4, -5

(x-3)(x-3)=0; x=3

Not factorable

Find the zeros of this quadratic. (Finding the zeros means to find the solutions.)

b=4/5, b=3

b=4, b=-3

b=1/5, b=3

b=4/5, b=-3

Solve by factoring:
x² - 9x = 0

0, 9

-9, 0

-9

10.

Factors AND find the solutions of x² + 2x – 3 = 0

(x - 2)(x + 1); x=2, x=-1

(x + 1)(x - 3); x=-1, x=3

(x + 2)(x - 1); x=-2, x=1

(x - 1)(x + 3); x=1, x=-3

11.

What are the zeros of the function below? (Finding zeros is the same as finding the solutions.)

(x - 6)(2x + 4) =0

x = -6, x = -4

x = 6, x = -2

x = 4, x = 6, x =2

cannot be determined

12.

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

Get factored form

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

Make it equal 0 by subtracting 3 on each side

Type it all in a calculator.

13.

Solve by factoring: x² = 7x + 18

-7 and -18

9 and 2

9 and -2

2 and 7

14.

What is this formula?

This is the speed of light formula.

This is the quadratic formula.

This is the zero product property.

This is scary.

15.

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

-10 & -4

-4 & 10

-8 & 4

8 & -4

16.

Solve the following for x by using the Quadratic Formula

2x²+6x=7

17.

What is the standard form for a Quadratic function?

ax²+ bx = - c

x = -b ± √(b²-4ac) / 2a

ax² + bx + c = 0

y = mx + b

18.

What is name of the graph of a Quadratic Equation?

Line

Parbola

Parabola

19.

What is the greatest number of solutions that a Quadratic Equation can have?

20.

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

-8, 5

-40, -1

5, 8

-8, -5

21.

Use the Quadratic Formula to solve the Quadratic Equation.

x² + 4x - 9 = 0

-2 ± √13

-2 ± 2√7

-2 ± √7

-2 + √7

22.

Solve by the Quadratic Formula:

$-12q^2+3q+7=0$

$\frac{-3\pm\sqrt{345}}{24}$

$\frac{3\pm\sqrt{345}}{-24}$

$\frac{3\pm\sqrt{345}}{24}$

$\frac{3\pm i\sqrt{39}}{24}$

23.

Solve x² - 5x + 10 = 0

(5 - i√15)/2 , (5 + i√15)/2

(5 - √15)/2 , (5 + √15)/2

(5 - i√65)/2 , (5 + i√65)/2

(5 - √65)/2 , (5 + √65)/2

24.

Solve for x:

x = {-4, -1}

x = {-1, -4}

x = {2+i, 2-i}

x = {-2+i, -2-i}

25.

In the equation
y = x² +5x +7, match each leading coefficient with its correct letter

a=0, b=5, c=7

a=1, b=5, c=7

a=7, b=5, c=1

Reset

Solving Quadratics by Factoring and Quadratic Formula

Total questions: 25

Worksheet time: 6hrs 15mins

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