Alg II Unit 4-6 Completing the Square
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Transcript of Alg II Unit 4-6 Completing the Square
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)