Name______________________________
Date: _________________ Block:_______
Ms. Gallagher
Warm Up
1. Factor the following trinomial expressions
a. x2 – 4x + 4
b. x2 + 10x + 25
c. x2 – 14x + 49
2. What number do you need to add to the trinomial to make it a perfect square
trinomial?
a. x2 + 6x + _____
b. x2 – 12x + ______
c. x2 – 16x + ______
Notes Completing the Square
Completing the square is useful for turning a quadratic function in standards form into
vertex form. Vertex form is useful for graphing quadratics using transformations!
Steps to completing the square:
1.
2.
3.
4.
Move the constant term to the right
Factor out the “a”
Cut “b” in half and square it. Add this value to both sides.
Factor the left side (perfect square trinomial)
Why change to vertex form?
**Easier to graph quadratic functions**
**Can solve by taking the square root of both sides!**
Example One Change from standard form to vertex form
y = x2 – 12x + 4
y = x2 + 8x + 1
You try Change from standard form to vertex form
y = x2 + 6x + 4
y = x2 – 4x – 2
Example Two Change from standard form to vertex form
y = 2x2 + 8x – 3
y = 3x2 – 6x + 8
Example Three Solve by completing the square
0 = x2 + 6x – 12
0 = 4x2 – 8x + 9