Solving equations of the form : ax2 + bx + c = 0. What we
have seen so far --
Method 1: Factoring :
Example 1: 2x2 – x – 1 = 0
factor: (2x + 1)(x – 1) = 0
solve:
2x + 1 = 0 
x – 1 = 0
x = –1/2 x = 1
Method 2: Square Root Property:
Example 2:
Method 3: Completing the Square:
Adding a new method
Method 4: Quadratic Formula
Development of the Quadratic Formula:
Given: ax2 + bx + c = 0
Step 1: Coefficient of x 2 is not 1 so divide it out:
Step 2: X's on the left and numbers on the right
Step 3: Complete the square on the x's and add the result
to both sides
Take 
which is
Put the right hand side over a common denominator of 4a2
Step 4: Use the Square Root Property to Solve
In Exercises 1-18, solve each equation using the quadratic
formula. Simplify, if possible.
Step 1: Write the equation in standard form: ax2 + bx + c = 0
Step 2: List a, b, and c
Step 3: Place those numbers into the quadratic formula
Step 4: Simplify the answer
The Discriminate:__________________
It will de termine the TYPE or solution the quadratic equation will have.
Look at:
In Exercises 19 - 30, compute the discriminate. Then
determine the number and type of
solutions for the given equation.
The Zero - Product Principle in Reverse
If A = 0 or B = 0, then AB = 0
Example: Write a quadratic equation with the given solution set:
{ 3, – 2}
The above says:
x = 3 or x = – 2
x – 3 = 0 or x + 2 = 0
(x – 3)(x + 2) = 0
x2 – x – 6 = 0
