Completing the Square

Solving Square Root

100

Solve the equation. (x-2)²=16

-2 and 6

200

Solve the equation. (x-3/2)²=13

3/2±√13

300

Solve the equation. (x-5)²=16

1 and 9

400

Solve the equation. 4(x-1)²=12

1±√3

500

Solve the equation. -2(x+4)²=12

-4±i√6

Perfect Square Trinomials

100

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

x²+14x+49=(x+7)²

200

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

x²-12x+36=(x-6)²

300

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

(x+13)²

400

Is x²-5x+25 a perfect square trinomial?

No

500

Complete the square for each expression. Write the resulting expression as a binomial squared with fractions not decimals. 

 x²-9x+?

x²-9x+81/4=(x-9/2)²

Solving Complete the Square

100

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

3±√5

200

Solve the equation by completing the square. 2x²-20x=8

5±√29

300

Solve the equation by completing the square. 

x²=24-4x

-2±2√7

400

Solve the equation by completing the square.

10x+x²=42

-5±√67

500

Solve the equation by completing the square. 2x²+12x+2=0

x= ±2√2-3

Vertex Form

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

Write each function in vertex form, and identify its vertex. 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+36x+25

h(x)=9(x+2)²-11 (-2,-11)

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)

Miscellaneous

100

Vertex form for a quadratic function.

f(x)=a(x-h)²+k

200

What must be add to the expression x²+bx to complete the square?

(b/2)²

300

What is the vertex of  f(x)=-4(x+55)²+100

(-55,100)

400

Factor 4x²-25

(2x+5)(2x-5)

500

factor 36x²-1

(6x+1)(6x-1)