Optimization & Quadratics Honors Analysis

6 𝑎 2 𝑏 4 −8 𝑎 3 𝑏 FACTOR Completely

−32𝑥 3 +50𝑥 𝑦 2 Factor Completely

12 𝑥 3 +10 𝑥 2 −12𝑥 FACTOR COMPLETELY

3 𝑥 3 +15 𝑥 2 +2𝑥+10 FACTOR COMPLETELY

Expand each perfect square What patterns do you notice?? (𝑥+3) 2 (𝑥−4) 2 (𝑥+5) 2 (𝑥+𝑦) 2 Expand each perfect square What patterns do you notice??

What value of k makes each expression a perfect square trinomial? 𝑥 2 −8𝑥+𝑘 𝑥 2 −5𝑥+𝑘 9𝑥 2 +18𝑥+𝑘 What value of k makes each expression a perfect square trinomial?

Complete the square – write in vertex form 𝑦=𝑥 2 −6𝑥+1 𝑦= 2𝑥 2 −10𝑥+3 Complete the square – write in vertex form

Solve quadratics by completing the square

Solve by completing the square

Writing in Vertex Form

Vertex Form

Vertex Form

Vertex Form