Completing the Square

Perfect Square Trinomials Examples x2 + 6x + 9 x2 - 10x + 25 x2 + 12x + 36

Creating a Perfect Square Trinomial In the following perfect square trinomial, the constant term is missing. X2 + 14x + ____ Find the constant term by squaring half the coefficient of the linear term. (14/2)2 X2 + 14x + 49

Perfect Square Trinomials Create perfect square trinomials. x2 + 20x + ___ x2 - 4x + ___ x2 + 5x + ___ 100 4 25/4

Quadratic Functions 2x2 + 3x - 5 GENERAL form: If a>0 it opens UP If a<0 it opens DOWN STANDARD or VERTEX form: where is the vertex. 2x2 + 3x - 5

by “Completing the Square” Changing to Standard Form by “Completing the Square” Step 1: Group the 1st 2 terms f(x) = x2 + 8x + 11 f(x) = (x2 + 8x) + 11 Step 2: Add & subtract blanks f(x) = (x2 + 8x + _) + 11 - _ 42 42 Step 3: ½ the middle term squared f(x) = (x + 4)2 + 11 - 16 Step 4: factor Step 5: simplify f(x) = (x + 4)2 - 5

Step 1: Group the 1st 2 terms f(x) = 2x2 + 8x + 7 Step 1: Group the 1st 2 terms f(x) = (2x2 + 8x) + 7 Step 2: Factor out the 2 f(x) = 2(x2 + 4x) + 7 f(x) = 2(x2 + 4x + _) + 7 - _(2) 22 22 f(x) = 2(x + 2)2 + 7 - 8 f(x) = 2(x + 2)2 - 1

f(x) = -x2 - 4x + 21 YOUR TURN f(x) = -(x2 + 4x + _) + 21 - _(-1) 22 22 f(x) = -(x + 2)2 + 21 + 4 f(x) = -(x + 2)2 + 25