5.5 – Completing the Square

Algebra 2

Wednesday Warm-Up

•Coach Books• pg. 11 #28-30

28.G29.B30.H

Objectives

• Solve a quadratic equation by completing the square

What is “Completing the Square?”

• Completing the square is a process that allows you to write an expression of the form x² + bx as the square of a binomial.

• "Completing the square" is one of a large number of algebraic manipulations that one can use to convert an algebraic expression into a simpler form. The whole subject of algebra has to do with solving algebraic equations. So like the quadratic formula, and various other techniques for solving algebraic expressions, the motive is to obtain an expression that is easy to solve an algebraic equation with the minimum amount of pain and discomfort.

What’s the point?

• Completing the square is a useful thing to do when:• We want to find

information quickly … such as for graphing.

• We want to solve a quadratic equation but it does not factor.

• We want to solve a quadratic equation but factoring is tricky.

TIP: Completing the square is easiest when a = 1 and

b is an even number.

Where does this fit with what I already know?

Completing the Square

• In order to create a perfect square trinomial, you need to add , the area of the incomplete corner of the square.

x

x

5

5

x2 5x

5x

2 10 ? 0x x

2

2

b

2210

(5) 252

?

Completing the Square 2

2

bc

• Find the value of c that makes the expression a perfect square

trinomial.

Recall:

1) 2)2 7x x c 2 8x x c

16c 49

4c

Solving a Quadratic Equation if the Coefficient of x2 = 1• Steps:1. Isolate the x2 term (a) and the x term (b)2. Divide the x term (b) by 2, square it, and add it to

both sides3. Factor the perfect square trinomial4. Solve the equation for x

Solving a Quadratic Equation if the Coefficient of x2 = 1

EX 1) 2 10 3 0x x

5 2 7x

Solving a Quadratic Equation if the Coefficient of x2 = 1

EX 2) 2 6 8 0x x

3 17x

EX 3) 2 4 1 0x x

2 5x

Solving a Quadratic Equation if the Coefficient of x2 ≠ 1• Steps:1. Divide each side of the equation by the coefficient

of x2 term (a)2. Isolate the x2 term (a) and the x term (b)3. Divide the x term (b) by 2, square it, and add it to

both sides4. Factor the perfect square trinomial5. Solve the equation for x

Solving a Quadratic Equation if the Coefficient of x2 ≠ 1

EX 1) 23 6 12 0x x

1 3x i

Solving a Quadratic Equation if the Coefficient of x2 ≠ 1

EX 2) 25 10 30 0x x

1 5x i

EX 3) 23 24 27 0x x

4 7x

Homework/Reminders

• pgs. 286-287 #32-34, 47, 48, 55, 56

Quiz 5.4-5.6 on Tuesday, December 4th

5.5 – Completing the Square(Day 2)

Algebra 2

Challenge Problem• Solve by completing the

square.

23 12 16 0x x

2 32

3x i

Homework Check/Questions• Take out last night’s homework• Check your answers• Anything that is incorrect is worth asking about

Completing the Square

• Why do we use to complete the square?

Proof Without Words: Completing the Square

2

2

bc

Treasure Raffle• Complete the worksheet with a partner• Your pair will be given a number – write it down at

the top of your worksheet• Help each other out• Ask Mr. V for help if you are still struggling• Prizes will be raffled off at the end of class

Homework/Reminders

• pgs. 286-287 #35-37, 49, 51, 57, 58

Quiz 5.4-5.6 on Tuesday, December 4th