Quadratic Equations

Factoring

100

Solve by factoring:
x² - 5x - 14 = 0

(x+2)(x-7)
x = -2 or x = 7

200

Solve by factoring:
x² - 16x + 63 = 0

(x - 9)(x - 7)
x = 9 or x = 7

300

Solve by factoring: 2x² = 72

2(x - 6)(x + 6)
x = 6 or x = -6

400

Solve: 5 - 17x = 2x² + 26

{-3/2 , -7 }

500

Solve: 7(x²+1) = 4(8x+15) + 7

7x² - 32x - 60 = 0
(7x + 10)(x - 6) = 0
{ -10/7 , 6 }

Completing the Square

100

Find c to complete the square:

x² + 6x + c

c = 9

200

Find c to complete the square:
x² + 9x + c

c = 81/4

300

Solve by completing the square:
x² - 4x - 98 = 0

{2 + √ 102 , 2 - √ 102 }

400

2x² - 24x + 46 = 0

{6 + √ 13 , 6 - √ 13 }

500

Solve by completing the square:
x² - 7x = 2

x = 7/2 + √ 57 / 2,
x = 7/2 - √ 57 / 2

Find the Roots

100

What does a root or zero look like on a graph?

Where the graph touches or crosses the x-axis
(an x-intercept)

200

Find the roots and sketch the graph:
f(x) = x² + 7x + 12

x = 3 and x = 4 are roots
Graph is concave up and passes through (3, 0) and (4, 0)

300

Find the zeros:
g(x) = x² - x - 56

(x - 8)(x + 7)
Zeros at x = 8 and x = -7

400

Find the roots and sketch the graph:
f(x) = -x² + 121

Double root at x = 11
Graph is concave down and bounces off x-axis at x = 11

500

Find the zeros:
h(x) = 6x² + 67x - 60

(6x - 5)(x + 12)
Zeros at x = 5/6 and x = -12

Square Roots

100

Solve by square root:
5x² + 12 = 62

&plusmn √ 10

200

(x - 2)² + 11 = 75

(10, -6)

300

77 = 5 - 2x²

No real solutions

400

55 = 5(x+2)²

-2  ± √  11

500

x² + 10x + x² - 2x = 8x - 32

No real solutions

Word Problems

100

Samantha threw a water balloon in the air and would like to find the water balloon's maximum height. What is Samantha trying to find? (x-intercept, y-intercept, x at vertex, or y at vertex)

y at vertex

200

Jennifer threw a ball in the air and wants to know how long her ball will take to hit the ground. What is Jennifer trying to find? (x-intercept, y-intercept, x at vertex, or y at vertex)

x-intercept

300

The height in feet of a bottle rocket is given by h(t)=160t −16t2, where t is the time in seconds. How long will it take for the rocket to return to the ground?

t = 10 seconds

400

What is the quadratic equation needed to maximize the area of a rectangle constructed with a perimeter of 44cm? (hint: draw a picture)

A = -x^2+22x

500

-16t^2+64t+80 represents the height in metres of a rocket at t time in seconds. What was the rocket's initial height? (y-intercept)

y = 80m