Monday May 6 th 2013 Honors Algebra

May 6 th The Quadratic Formula Why didn’t we learn this first ?

Quadratic Formula There once a negative boy who was all mixed up so he went to this radical party. Because the boy was square, he lost out on 4 awesome chicks so he cried his way home when it was all over at 2 AM.

Quadratic Formula IF THEN

THE QUADRATIC FORMULA 1.When you solve using completing the square on the general formula you get: 2.This is the quadratic formula! 3.Just identify a, b, and c then substitute into the formula.

WHY USE THE QUADRATIC FORMULA? The quadratic formula allows you to solve ANY quadratic equation, even if you cannot factor it. An important piece of the quadratic formula is what’s under the radical: b 2 – 4ac This piece is called the discriminant.

WHY IS THE DISCRIMINANT IMPORTANT? The discriminant tells you the number and types of answers (roots) you will get. The discriminant can be +, –, or 0 which actually tells you a lot! Since the discriminant is under a radical, think about what it means if you have a positive or negative number or 0 under the radical.

WHAT THE DISCRIMINANT TELLS YOU! Value of the DiscriminantNature of the Solutions Negative2 imaginary solutions Zero1 Real Solution Positive – perfect square 2 Reals- Rational Positive – non- perfect square 2 Reals- Irrational

Understanding the discriminant Discriminant # of real roots 2 real roots 1 real roots No real roots

#1 Solve using the quadratic formula.

#2 Solve using the quadratic formula

Solve using the quadratic formula

#3 Solve using the quadratic formula

#4 Solve using the quadratic formula

#5 Solve using the quadratic formula

The Discriminant Discriminant In the quadratic formula, the expression underneath the radical that describes the nature of the roots.

Understanding the discriminant Discriminant # of real roots 2 real roots 1 real roots No real roots

#6 Using the discriminant

1) 2) 3)

#7 Using the discriminant

Using the discriminant 8. 9.

#8 Using the discriminant

#9 Using the discriminant