Solving Quadratic Equations

Factoring

100

x² - 1 = 0

{-1, 1}

200

Solve the following quadratic equation by factoring:

9x² - 81x = 0

{0, 9}

300

Solve the following quadratic equation by factoring.

 n² - 7n + 6=0

{6, 1}

400

Solve the following quadratic equation by factoring. 

b² - 8b = 36 - 8b

{-6,6}

500

Solve the following quadratic equation by factoring. 

9x² + 5x - 5= 6x² + 3x

{-5/3, 1}

Forms

100

What info does this form tell you?

y = x² + 6x - 9

Y intercept (0,-9)

200

What does this form tell you?

y = 2(x-3)² -2

Vertex (3, - 2)

300

What are the intercepts?

y = -5(x-1)(x + 2)

(1,0) (-2,0)

400

What is the axis of symmetry?

y = -2x² - 3

x = 0

500

 What is the x intercept?

x² - 8x + 16 = y

(4,0)

Imaginary

100

sqrt (-25)

5i

200

(3 - i) + (3i + 5) 

8 + 2i

300

2i sqrt - 49

-14

400

(2 - 4i) - (-6 + 3i) 

8-7i

500

(-3 + 2i)(6 + 3i)

-24 + 3i

Quadratic Formula

100

What is the quadratic formula?

x =( -b pm sqrt(b^2 - 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 + 6 = 0

(9 pm sqrt(57))/2 = x

400

Solve the following quadratic equation by using the quadratic formula: x² - 6x + 12 = 0

3 +- iroot3

500

Solve the following quadratic equation by using the quadratic formula: 

2x² +x =-12 

x = (-1 pm sqrt(95))/4