1. Warm-up 8-1
Given solve for a
Solve

2. Lesson 8-1 Introducing Quadratic Equations
Objectives
Students will:
Solve quadratic equations by factoring and completing the square

3. Quadratic Equations
Form: ax2 + bx + c = 0
Example: 16t2 + v0t – h = 0
v0 = initial velocity; h = height
Anything affected by gravity will be quadratic
Solving Quadratics
x2 & x terms: Just x2 term:
Set equal to zero
Factor completely
Set factors equal to 0
Isolate x2 term
Square root both sides

4. Example 1 Example 2
2x2 + 7x = x2 + 3 = 0
Try to solve: x2 – 2x – 5 = 0
We need a technique to solve these

5. Completing the Square
Strategy: Add something to both sides to make a perfect square trinomial
Method: x2 – 2x – 5 = 0
Move constant term
x2 – 2x = 5
Add “square the half” the middle
term to both sides
x2 – 2x + 1 = 6
Factor trinomial as perfect square
(x – 1)2 = 6
Square root both sides
x – 1 =
Solve for x
x = , 1 -

6. Example 3 Example 4
x2 + 10x + 23 = 0 x2 + 7y + 12 = 0
HW 93 & 94