BM 9: Solving Quadratic Equations

What is on the benchmark tomorrow?

WAYS TO SOLVE A QUADRATIC EQUATION ax² + bx + c = 0

• Must be in standard form, =0• Methods:

– Graphing– Factoring– Quadratic formula

By Graphing

By looking at the roots, we can get the solutions.x = -2, 4

f(x) = x2 – 2x – 8

Line of Symmetry (to find vertex):

x b2a

Factoring

*Factor out GCF, if one* Check for Difference of Squares:

x2 – y2 = (x + y)(x – y)

1) Easy (a=1)-make ac-b chart-write answer: (x + )(x + )

2) Long (a>1)-make ac-b chart-split the middle term-factor by grouping

Solving a Quadratic Equation by Factoring

1) Factor completely.2) Use the ZPP: set each factor with a

variable equal to zero3) Solve each equation

BACK

Solving using the Quadratic formula

1) Calculate discriminant first (b2 – 4ac)-tells us how many solutions

2) Find solutions using the formula (can be rational or irrational)

x b b2 4ac

2a