This document provides instruction on solving quadratic equations by completing the square. It begins by explaining that completing the square allows one to factor a trinomial as the square of a binomial. It then provides examples of completing the square to solve quadratic equations in various forms, including perfect square trinomials and those requiring the addition of (b/2)2. The document demonstrates transforming equations into vertex form by completing the square. Students are assigned practice problems applying these techniques.

1. 4-6 COMPLETING THE SQUARE
Chapter 4 Quadratic Functions and Equations
©Tentinger

2. ESSENTIAL UNDERSTANDING AND
OBJECTIVES
 Essential Understanding: completing a perfect
square trinomial allows you to factor the completed
trinomial as the square of a binomial
 Objectives:
 Students will be able to:
 Solve equations by completing the square
 Rewrite functions by completing the square

3. IOWA CORE CURRICULUM
 Algebra
 Reviews A.REI.4b. Solve quadratic equations in
one variable.
 Solve quadratic equations by inspection taking square
roots, completing the square, the quadratic formula and
factoring, as appropriate tot eh initial form of the
equation. Recognize then the quadratic formula gives
complex solutions and write them as
a±bi for real numbers a and b.

4. SOLVING BY FINDING SQUARE ROOTS FOR
THE FORM AX2 = C
 4x2 + 10 = 46
 Step 1: rewrite in the form ax2 = c
 Step 2: isolate x
 Step 3: find the square root.
 What is the solution of each equation?
 7x2 – 10 = 25
 2x2 +9 = 13

5. EXAMPLE
 Determining Dimensions
 While designing a house, an architect
used windows like the one shown here.
What are the dimensions of the window
if it has 2766 square inches of glass?
 Find the area of the rectangular part
 Find the area of the semicircle (hint use the formula
to find the area of a circle)
 Solve for x.

6. EXAMPLE
 The lengths of the sides of a rectangular window
have a ratio of 1.6 to 1. The area of the window is
2822.4 inches squared. What are the window
dimensions?

7. PERFECT SQUARE TRINOMIAL EQUATION
 Solving a Perfect Square Trinomial Equation
 x2 + 4x + 4 = 25
 x2 – 14x + 49 = 25
 x2 +12x + 36 = 9

8. WHEN YOU DON’T HAVE A PERFECT SQUARE
TRINOMIAL
 Complete the Square using form x2 + bx
 x2 + bx + (b/2)2 = (x + b/2)2
 x2 – 10x
 x2 + 6x
 x2 + 14x

9. WHEN YOU DON’T HAVE A PERFECT SQUARE
TRINOMIAL
 Complete the Square using form x2 + bx = c
 3x2 – 12x + 6 = 0  3x2 – 12x = -6
 2x2 – x + 3 = x + 9

10. VERTEX FORM
 Completing the Square to write the equation in
Vertex Form
 y = x2 + 4x – 6
 y = x2 – 3x – 6

11. HOMEWORK
 Pg. 237 – 238
 # 12 – 51 (3s)