4-6 COMPLETING THE SQUAREChapter 4 Quadratic Functions and Equations

©Tentinger

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

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.

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

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.

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?

PERFECT SQUARE TRINOMIAL EQUATION

Solving a Perfect Square Trinomial Equation

x2 + 4x + 4 = 25

x2 – 14x + 49 = 25

 x2 +12x + 36 = 9

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 

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

VERTEX FORM

Completing the Square to write the equation in Vertex Form

y = x2 + 4x – 6

y = x2 – 3x – 6

HOMEWORK

Pg. 237 – 238 # 12 – 51 (3s)