Completing the Square

Solving Quadratics

100

Solve the equation. (x-2)²=16

x=6 and x=-2

200

Solve the equation. (x-3)²=13

x=-0.60555 x=6.056

300

Solve the equation. x²-10x+25=16

x=1 and x=9

400

Solve the equation. x²-2x+1=3

x=-0.73205 x=2.7321

500

Solve the equation. x²-2√3+3=16

x=-4.0576 x=4.0576

Complete the square

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 + 26x + ?

x² + 26x + 169 

(x+13)²

400

Complete the square for each expression. Write the resulting expression 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

Standard form-->Vertex form

100

Convert to vertex form by completing the square:

y = x² + 16x + 71

y = (x + 8)² + 7

200

Convert to vertex form by completing the square:

y = x² − 2x − 5

y = (x − 1)² − 6

300

Convert to vertex form by completing the square:

y = x² + 4x

y = (x + 2)² − 4

400

Convert to vertex form by completing the square:

y = x² + 10x + 33

y = (x + 5)² + 8

500

Convert to vertex form:

y = (x + 5)(x + 4)

y = (x + 9/2)² − 1/4

Solving by Completing the Square

100

Solve by completing the square:

a² + 14a − 51 = 0

x=3 and x=-17

200

Solve by completing the square:

x² − 12x + 11 = 0

x=11 and x=1

300

Solve by completing the square:

n² − 2n = 3

x=3 and x=-1

400

Solve by completing the square:

k² − 12k = -23

k=2.3944 and k=9.6056

500

Solve by completing the square:

b² + 2b = −20

No Solution (Parabola is above x axis)

Quadratic Trivia

100

Identify the vertex:

y=(x-3)² + 4

Vertex: (3,4)

200

What is the name of the shape of a quadratic function

Parabola

300

Explain how to find....

x-intercepts

y-intercepts

vertex & Line of symmetry

Given the equation: y=(x+3)² -4

x-int: pug in 0 for y, solve for x by adding 4 to both sides take the square root of both sides. Then set up two equations to solve for x.

y-int plug in 0 for x and solve for y.

vertex: look at equation and identify (-3,-4)

Line of symmetry look at x value of vertex and state: x=-3

400

When is Mr. A's Birthday

April 7th

500

. You are trying to dunk a basketball. You need to jump 2.5 ft in the air to dunk the ball. The height that your feet are above the ground is given by the function

 h(t) = -16t² + 12t.

 What is the maximum height your feet will be above the ground? Will you be able to dunk the basketball?

No, he will only be jumping 2.25ft in the air.