Algebra: Solving Quadratic Equations

Discriminant

100

What is the formula to find the discriminant?

b^2-4ac

200

What is the discriminant:

5b^2 + b − 2 = 0

41

300

What is the discriminant:

−4m^2 − 4m + 5 = 0

96

400

Using the discriminate, which method should you use to solve this quadratic? 

9m^2 + 6m + 6 = 5

Factoring (discriminate equals zero)

500

Using the discriminate, which method should you use to solve this quadratic?

−4r^2 − 4r = 6

Quadratic formula (discriminate is -80)

Solve with Factoring

100

Solve the following quadratic equation by factoring. 

x² - 6x + 5 = 0

x= {1, 5}

200

Solve the following quadratic equation by factoring:

9x² - 81x = 0

x = {0, 9}

300

Solve the following quadratic equation by factoring.

 3n² - 25n + 28=0

x= {4/3, 7}

400

Solve the following quadratic equation by factoring. 

9x² + 10x - 30= 7x

x= {5/3, -2}

500

Solve the following quadratic equation by factoring. 

28b² - 348 =-5

x= {-7/2, 7/2}

Completing the Square

100

Solve the following quadratic equation by completing the square: 

x² + 6x = -8

x = {-4, -2}

200

Solve the following quadratic equation by completing the square: 

x² - 6x = -5

x = {1, 5}

300

Solve the following quadratic equation by completing the square: 

x² - 2x = 24

x = {-4, 6}

400

Solve by completing the square:

2x^2-16x=-30

x={3,5}

500

Solve by completing the square:

x² + 8x - 20 = 0

x = {-10, 2}

Solving with Square Roots

100

When is it best to use the square root method for solving quadratics?

When there is no 'b' term.

200

Solve using square roots:

x^2-81=0

x=+-9

300

Solve using square roots:

2x^2-200=0

x=+-10

400

Solve using square roots:

5x^2-11=234

x=+-7

500

Solve using square roots:

4x^2-39=10

x=+-7/2

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:

6x² - 19 = 5

x = ±2

300

Solve the following quadratic equation by using the quadratic formula: x² -2x -48 = 0

x = -6, 8

400

Solve the following quadratic equation by using the quadratic formula:

6x^2+17x+12=0

x= -3/2, -4/3

500

Solve the following quadratic equation by using the quadratic formula:

10x^2-19=5

x= 

+-(2sqrt15)/5