Factoring
Completing the Square
Find the Roots
Square Roots
Miscellaneous
100
Solve by factoring:
x2 - 5x - 14 = 0
(x+2)(x-7)
x = -2 or x = 7
100
Find c to complete the square:
x2 + 6x + c
c = 9
100
What does a root or zero look like on a graph?
Where the graph touches or crosses the x-axis
(an x-intercept)
100
Solve by square root:
5x2 + 12 = 62
&plusmn √ 10
100

Identify a, b and c in this equation: -x2 - 2x + 12

a = -1, b = -2, c = 12

200
Solve by factoring:
x2 - 16x + 63 = 0
(x - 9)(x - 7)
x = 9 or x = 7
200
Find c to complete the square:
x2 + 9x + c
c = 81/4
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)
200
(x - 2)2 + 11 = 75
{10, -6}
200

Simplify:  (2x3)-2  

No negative exponents in your answer.

1/(4x6)

300
Solve by factoring: 2x2 = 72
2(x - 6)(x + 6)
x = 6 or x = -6
300
Solve by completing the square:
x2 - 4x - 98 = 0
{2 + √ 102 , 2 - √ 102 }
300
Find the zeros:
g(x) = x2 - x - 56
(x - 8)(x + 7)
Zeros at x = 8 and x = -7
300
77 = 5 - 2x2
No real solutions
300

Find (fg)(x) if f(x) = x+2 and g(x) = 2x+1.

2x2+6x+2

400
Solve: 5 - 17x = 2x2 + 26
{-3/2 , -7 }
400
2x2 - 24x + 46 = 0
{6 + √ 13 , 6 - √ 13 }
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
400
55 = 5(x+2)2
-2 &plusmn √ 11
400

Find (fog)(2) if f(x) = 3x-1 and g(x) = 2x+5

26

500
Solve: 7(x2+1) = 4(8x+15) + 7
7x2 - 32x - 60 = 0
(7x + 10)(x - 6) = 0
{ -10/7 , 6 }
500
Solve by completing the square:
x2 - 7x = 2
x = 7/2 + √ 57 / 2,
x = 7/2 - √ 57 / 2
500
Find the zeros:
h(x) = 6x2 + 67x - 60
(6x - 5)(x + 12)
Zeros at x = 5/6 and x = -12
500
x2 + 10x + x2 - 2x = 8x - 32
No real solutions
500

Find the equation of the line that is parallel to y=3x+1 and goes through the point (2, 10).

y=3x+4

M
e
n
u