1. Completing the Square

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

3. 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) X2 + 14x + 49

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

5. 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

6. 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 + _) _ 42 42
Step 3: ½ the middle term squared
f(x) = (x + 4)
Step 4: factor
Step 5: simplify
f(x) = (x + 4)2 - 5

7. 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 + _) _(2) 22 22
f(x) = 2(x + 2)
f(x) = 2(x + 2)2 - 1

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