Completing the Square

✎EXAMPLE 1✎

100

Solve the equation. (x-2)²=16

-2,6

200

Solve the equation. (x-3/2)²=13

±√13+3/2

300

Solve the equation. x²-10x+25=16

1,9

400

Solve the equation. x²-2x+1=3

1±√3

500

Solve the equation. x²-2√3+3=16

±4+√3

☆EXAMPLE 2☆

100

Complete the square for each expression. Write the resulting express as a binomial squared. x²+14x+?

x²+14x+49=(x+7)²

200

Complete the square for each expression. Write the resulting express as a binomial squared. x²-12x+?

x²-12x+36=(x-6)²

300

Complete the square for each expression. Write the resulting express as a binomial squared. x²+338x+?

(x+13)²

400

Complete the square for each expression. Write the resulting express as a binomial squared. 

x²-(√4 /2 )x+?

x²-x+1/4=(x-1/2)²

500

Complete the square for each expression. Write the resulting express as a binomial squared. x²-9x+?

x²-9x+81/4=(x-9/2)²

♡EXAMPLE 3♡

100

Solve the equation by completing the square. x²-6x=-4

3±√5

200

2x²-20x=8

5±√29

300

x²=24-4x

-2±2√7

400

10x+x²=42

-5±√67

500

a) Solve 2x²+12x+2=0, b) Show your classmate how to use the graphing calculator to verify the answer.

x= ±2√2-3

☃EXAMPLE 4☃

100

Write each function in vertex form, and identify its vertex. f(x)=x²-4x+13

f(x)=(x-2)²+9 (2,9)

200

Write each function in vertex form, and identify its vertex. g(x)=x²-10x+11

f(x)=(x-5)²-14 (5,-14)

300

h(x)=3x²-12x-4

h(x)=3(x-2)²-16 (2,-16)

400

Write each function in vertex form, and identify its vertex. h(x)=9x²+4x+25

h(x)=9(x+1)²-12 (-1,-12)

500

Write each function in vertex form, and identify its vertex. f(x)= -2x²+8x=4

f(x)=-2(x-2)²+12 (2,12)

Mr. Robertson

100

What is Mr. Robertson's favorite fruit?

Pineapple

200

What is Mr. Robertson's number 1 listened to artist in 2025?

Sublime

300

What is Mr. Robertson's dog's name?

Kona

400

Mr. Robertson is vacationing in what location for Spring Break?

Orlando, Florida

500

What is Mr. Robertson's favorite kind of pie?

Key Lime Pie