Warm-up 8-1 Given solve for a Solve

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

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

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

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 + , 1 -

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