+ Completing the Square. + In your notes: Simplify the following: 1. 2. (5 – 3i)(4 + 2i) 3.

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Presentation transcript:

+ Completing the Square

+ In your notes: Simplify the following: (5 – 3i)(4 + 2i) 3.

+ Complex Numbers: Operations 1. (2 + 3i)(2 – 3i) 2. 5i i 3. (7 – 4i) – (10 + 2i)

+ Solve using the quadratic formula 1. 4x 2 + 2x – 6 = 0 2. x 2 + 5x – 2 = 0

+

+ 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 x x 2 – 16x x x + 81

+ Solving a Perfect Square Trinomial We can solve a Perfect Square Trinomial using square roots. x x + 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.

+ Solving by Competing the Square Rewrite in Vertex Form: Then solve for x! 1) x 2 + 6x + 8 = 0

+ 2) x 2 – 12x + 5 = 0

+ 3) x 2 – 8x + 36 = 0

+ 4) x 2 + 2x – 3 = 0

+ 5) x x – 22 = 0

+ Classwork and Homework Completing the Square