5.8 Solving Quadratic Funtions by Completing the Square 1/28/2013

Vocabulary Perfect Square Trinomial: Whenever you multiply a binomial by itself, the resulting trinomial is called a perfect square trinomial Example: x+1 This is the area of this square

Vocabulary Completing the Square : The process of adding a constant c to the expression x 2 + bx to make it a perfect square trinomial (PST) How? By adding to x 2 + bx What is it used for: Converting equations from standard form to vertex form. To solve quadratic functions when “Big X” does not work! Factored form of PST: The square of 2 binomials

Review Equation of a Parabola in VERTEX FORM: Where (h, k) is the vertex

Steps for completing the square y = x 2 + bx + c Standard form : y = x 2 + bx + c ( ) This is a PST Factored form of PST:

Example 1 y = x 2 + 6x + 5 Rewrite y = x 2 + 6x + 5 in Vertex Form and determine the vertex. ( ) 1.Put ( ) around x 2 + 6x and move +5 outside ( ) 2.Take half of 6 and square it. Add 9 to the ( ) and subtract 9 from Factor the PST in ( ) and simplify Vertex (-3, -4) This is a PST Factored form of PST:

Example 2 y = x 2 - 6x + 10 Rewrite y = x 2 - 6x + 10 in Vertex Form and determine the vertex. ( ) 1.Put ( ) around x 2 - 6x and move +10 outside ( ) 2.Take half of 6 and square it. Add 9 to the ( ) and subtract 9 from Rewrite what’s in the ( ) as (x - 3) 2 Vertex (3, 1)

Checkpoint Use Completing the Square Write in vertex form. Then identify the vertex. = x 2x 2 8x8x+19 – y ANSWER = y 3;3; ()2)2 4x – + () 4, 3

Homework: 5.8 p.271 #15-20