Quadratic Formula
Completing the Square
Factoring
Discriminant
Word Problems
100
Solve using Quadratic Formula:
x2 + 6x = 14
x = -3 +- sqrt23
100
Solve by completing the square: x2 – 8x + 5 = 0
x = 4+- sqrt11
100
Factor: 
(x-4) (x+8)
100
What is the discriminant of a quadratic?
b2 - 4ac
100
The sum of two numbers is 12 and their product is 35. What are the two numbers?
m = 5 and m = 7. The two numbers are 5 and 7
200
Solve using Quadratic Formula:
8x2 = 15 - 14x
x =
x = 3/4 or -5/2
200
Solve by completing the square: x2 + 12x + 4 = 0
x = -6+-4sqrt2
200
Factor: 
(3x+2) (4x-1)
200
Find the discriminant.
5t^2 + 6t + 7 = 0
= 6^2 - 4(5)(7)
= 36 - 140
= -104
200
One number is the square of another. Their sum is 132. Find the numbers.
-12 and 144 or 11 and 121.
300
Solve using Quadratic Formula:
2x2 - 7x = 5
x = (7 +- sqrt89)/4
300
Solve by completing the square: 3x2 – 12x – 7 = 0
x = 2+-sqrt57/3
300
Factor: x2 + x - 6
(x + 3) (x - 2)
300
Find the discriminant.
9v^2 - 9v - 9 = 0
= (-9)^2 - 4(9)(-9)
= 81 - (-324)
= 405
300
The difference of two numbers is 2 and their product is 224. Find the numbers.
-14 and -16 or 14 and 16.
400
3x2 = 10x + 4
x = (5 +- sqrt37)/3
400
Solve by completing the square: –2x2 – 12x – 9 = 0
x = -3 +- (3sqrt2)/2
400
Factor: x2 - 9x + 20
(x - 4) (x - 5)
400
Find the discriminant.
5w^2 + 3w - 9 = 0
= 3^2 - 4(5)(-9)
= 9 - (-180)
= 189
400
The number of mosquitoes in Anchorage, Alaska (in millions of mosquitoes) as a function of rainfall (in centimeters) is modeled by:
m(x)=-x^2+14x
The maximum mosquito population occurs when there is a rainfall of 7 centimeters.
500
Solve using Quadratic Formula:
1/6x2 + 4/3x - 2/3 = 0
x = -4+-2sqrt5
500
Solve by completing the square: 4x2 + 8x – 9 = 0
x = -1 +- sqrt13/2
500
Factor: x2 - 2x - 80
(x - 10) (x + 8)
500
Find the discriminant.
8u^2 + 8u + 2 = 0
= 8^2 - 4(8)(2)
= 64 - 64
= 0
500
The power generated by an electrical circuit (in watts) as a function of its current ccc (in amperes) is modeled by:
P(c)=-12c^2+120c
The maximum power occurs when the current is 5 amperes.