Objective
I can find zeros by completing the square
Warm Up
 Rewrite the following as perfect squares.
 1. x2 + 14x + 49
 ( _______)2
 2. x2 -2x + 1
 (________)2
Our goal
 What if you were asked to complete the pattern of a
perfect square.
 x2 + 20x + ____
(
)2
 OYO
 x2 -18x + ______
 (_______)2
This Process is called
“Completing the Square”
because our goal is to figure out
what number you need to create
a perfect square.
Not So Perfect Squares.
 Some equations aren’t as easy to see what value will
complete the square such as.
 For these we use
x2 + 9x +
 (b/2)2
 Look back at the previous complete the square problems,
how does the constant term of the factored binomial
relate to the middle term?
 What will be the factored form of this quadratic?
Check It Out! Example 2c
Complete the square for the expression. Write the resulting expression as a
binomial squared.
x2 + 3x +
Check Find the square of the binomial.
Find
Add.
Factor.
.
Why?
 We can use completing the square for two things.
 Solve quadratics by means of the square root property.
 Transform a function in standard form to vertex form.
 For this unit we will focus on solving equations by
completing the square.
You can complete the square to solve quadratic equations.
Solve the equation by completing the square.
x2 = 12x - 20
Solve the equation by completing the square.
18x + 3x2 = 45
Solve the equation by completing the square.
2x2 + 8x = 12
Solve the equation by completing the square.
5x2 + 10x – 7 = 0
OYO
Solve the equation by completing the square.
3x2 – 24x = 27