+ Unit 3 Classifying by terms and degrees Adding, Subtracting, Multiplying, Dividing Zeros in Factored Form End Behavior Factoring (GCF, a = 1, a ≠ 1) Special Cases (Difference of Squares, Sum and Diff of Cubes) Solving by Factoring Complex Numbers Completing the Square Vertex Form Deriving the Quadratic Formula Solving Special Cases
+ Perfect Square Trinomials Factor each of the following. What do you notice? 1. x 2 + 10x + 25 2. x 2 – 16x + 64 3. x 2 + 18x + 81
+ Solving a Perfect Square Trinomial We can solve a Perfect Square Trinomial using square roots. x 2 + 10x + 25 = 36
+ Solving a Perfect Square Trinomial x 2 – 14x + 49 = 81
+ What if it’s not a Perfect Square Trinomial? You can turn any quadratic binomial into a perfect square trinomial! If you have, you can “complete the square” by adding Note:
+ Completing the Square Using the formula for completing the square, turn each binomial into a perfect square trinomial. Then rewrite it has a square.
+ Completing the Square to Solve If an equation doesn’t have a perfect square Trinomial, we can use COMPLETING THE SQUARE to solve. Example: x 2 + 6x – 7 = 0 This is the original problem. Is it a perfect square? Move the constant over to the other side. Complete the square using That is, divide the x-term coefficient by two, square it, and add it to BOTH sides of the equation.