1. What is completing the square and why is it useful?
Algebra 2/Trig Name: __________________________
Section 5-5 Completing the Square Date: _____________ Block: ________
What is completing the square and why is it useful?
Completing the square is the process of writing x2 + bx as the square of a binomial.
To complete the square of x2+bx you need to add
But remember if you add to one side you need to add to the other side. This rule leads to
x2+bx = ( x + )2
** Useful for graphing in vertex form and solving unfactorable quadratics.**
When do we use it?
Usually when a=____ or everything is divisible by the “_____" value and b is _______.
**When we want to switch from standard to vertex form**
Steps:
1. Get x2 + bx on one side.
a. If x2 has a coefficient it must be factored out first.
2. Identify the b value. Find the __________ value. And then find ____________.
3. Add _________ to both sides.
4. Replace x2+bx+_____ with ( x +_____)2.
5. Square root both sides.
6. Solve for x.
Solve by completing the square. Example 1:
x2 - 10x - 3 = 0
Example 2:
9x2 – 18x = -3

2. What is Vertex Form? Solve by completing the square. Example 3:
x2 – 2x – 2 = 0
Example 4:
-3x2 - 12x + 9 = 0
What if b is not even?
What is Vertex Form?
Example 5:
x2+3x-1=0
Convert the following from standard form to vertex form
Example 7: y=x2+4x-1
Example 8: y= 4x2 +24x – 8