5.5 Completing the Square

What is Completing the Square?It allows us to write an expression x2

+ bx as the square of a binomial.

To make a “complete square” we need to add

So,

Solving EquationsTo solve by completing the square:

◦Get the x2 + bx part alone.◦Add (b/2)2 to each side.◦Factor (write as a binomial squared.)

◦Take square roots to solve for x.◦Simplify – NO DECIMALS!

Examples:Solve by completing the square:

Your Turn!Solve:

Using Complete The Square when a 1Divide both sides by a, then

complete the square.Solve:

Example:Solve by completing the square. 2x2 + 28x = 8

Your Turn!Solve by completing the square:

Writing Functions in Vertex FormUse complete the square to write

as

Example:Write in vertex form and find the

vertex.

Your Turn!Write in vertex form and find the

vertex.