AlgebraQUADRATIC FORMULA

For Solving When Factoring Won’t Work

The quadratic formula is used to solve quadratic equations when you cannot factor and solve using the roots.

This helpful formula works ALL the time but might not elicit an answer we can use (sometimes they are imaginary)

So What is this Wonder Formula?

𝑥=−𝑏±√𝑏2−4𝑎𝑐2𝑎

Huh??

Well that’s great but where do we have ???

Our quadratic equations all have the form:

Therefore, is the leading coefficient, is the coefficient of the middle term, and is the constant.

How Am I Going to Remember That?

What about a song?Adele VersionRow, Row, Row Your BoatPop Goes the WeaselOne Direction

Example

Example

AlgebraTHE DISCRIMINANT

What is the Discriminant?

The discriminant is the following expression:

b2-4ac(Hey that’s what is underneath

the radical in the quadratic formula!!)

Where do we find a,b and c?

cbxax 2

b2-4ac

So what?? Why do we care?

The discriminant is used to determine if there is 2, 1 or no real solutions to an equation

How can it do that??

If the Discriminant EQUALS 0, then there is one real solution to the quadratic equation

If the Discriminant is GREATER THAN 0, then there are two real solutions to the quadratic equation

If the Discriminant is LESS THAN 0, then there are no real solutions to the quadratic equation (only imaginary ones ).

Example:How many solutions does the following

quadratic equation have?

This is GREATER THAN 0, therefore there are 2 Solutions

Example:How many solutions does the following

quadratic equation have?

This is LESS THAN 0, therefore there are No Solutions

Example:How many solutions does the following

quadratic equation have?

This is EQUALS 0, therefore there is One Solution

Assignment 10-7