Solving Quadratic Equations

Factoring

100

Use the Zero Product Property to solve the following quadratic equation. (x - 7)(x + 2) = 0

x = 7 x = -2

200

Rewrite the quadratic equation in factored form: 

x² + x - 20 = 0 

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

300

If the equation  x(2x+4)=0 is true

What are the solutions?

x= 0

x= -2 

400

Solve the following quadratic equation by factoring. x² - 6x + 5 = 0

x = 5 x = 1

500

Solve the following quadratic equation by factoring. x² - 6x - 27 = 0

x = 9 x = -3

Difference of Squares

100

Solve the following quadratic equation by using square roots: x² = 4

x = 2 x = -2

200

Solve the following quadratic equation by using differences of squares 

x² - 121 = 0

+11 or -11

300

Solve the following quadratic equation by using difference of squares:  4x² - 400 = 0

x = 10 x = -10

400

Solve the following quadratic equation by using difference of squares:  x² -9 = -8

1 or -1

500

Solve the following quadratic equation by using difference of squares: 5x² + 3 = 128

x = 5 x = -5

Completing the Square

100

Solve the following quadratic equation by completing the square: x² + 6x = -8

x = -2 x = -4

200

Solve the following quadratic equation by completing the square: x² - 6x = -5

x = 1 x = 5

300

Solve the following quadratic equation by completing the square: x² - 2x - 24 = 0

x = -4 x = 6

400

Solve the following quadratic equation by completing the square: x² + 10x +16 = 0

x = -2 x = -8

500

Solve the following quadratic equation by completing the square: 2x² - 8x = 10

x = 5 x = -1

Quadratic Formula

100

What is the quadratic formula?

x = -b +- sqrt(b² - 4ac) /(2a)

200

Solve the following quadratic equation by using the quadratic formula: x² + 6x + 5 = 0

x = -1 x = -5

300

Solve the following quadratic equation by using the quadratic formula: x² - 9x + 20 = 0

x = 5 x = 4

400

Solve the following quadratic equation by using the quadratic formula: 2x² + 9x + 4 = 0

x = -1/2 x = -4

500

Solve the following quadratic equation by using the quadratic formula: 4x² - 17x - 15 = 0

x = 5 x = -3/4

Rational/ Irrational

100

What is a rational number?

A real number

Any fraction with a non-zero denominator

Any decimal that terminates

Any decimal that repeats 

200

Which of the following are NOT rational?

a) 0.666

b) 8.3

c) 2.3438279011042984765309

d) 16

2.3438279011042984765309

300

True or False

The SUM (+) of a rational number and a rational number is SOMETIMES rational. 

False; ALWAYS 

400

True or False

The sum of a rational and irrational number is ALWAYS irrational.

False; NEVER

500

True or False

The product (x) of a rational number and an irrational number is ALWAYS irrational. 

True; ALWAYS