Factoring
Factor: x2 + 10x + 24
(x+4)(x+6)
Identify the vertex by completing the square:
x2 + 6x + 8
(x+3)2 - 1
Vertex: (-3, -1)
Multiply then simplify:
(2x + 5)(x - 3)
2x2 - x - 15
What is the quadratic formula?
x =( -b pm sqrt(b^2 - 4ac)) /(2a)
Write down the growth and exponential decay formulas
Growth: y= a(1 + r)x
Decay: y= a(1 - r)x
Factor: x2 + 13x - 48
(x + 16)(x - 3)
Identify the vertex by completing the square:
x2 - 6x + 5
(x - 3)2 - 4
Vertex: (3, -4)
2x + 8x - 2 + 3x2 + 10
3x2 + 10x + 8
Solve the following quadratic equation by using the quadratic formula, then state if the roots are real or complex.
x2 + 6x + 5 = 0
x = -1, x = -5
REAL
In 1985, there were 285 cell phone subscribers in the small town of Centerville. The number of subscribers increased by 75% per year after 1985. How many cell phone subscribers were in Centerville in 1994?
Approximately 43,872 subscribers
Factor: x2 - 81
(x + 9)(x - 9)
Identify the vertex by completing the square:
x2 - 2x + 24
(x - 1)2 + 23
Vertex: (1, 23)
Simplify:
(2x2 + 4x - 7) + (8x2 - 3x - 5)
10x2 + x - 12
Solve the following quadratic equation by using the quadratic formula.
x2 - 9x + 6 = 0
(9 pm sqrt(57))/2
OR
x=8.27, x=0.73
REAL
An adult takes 400 mg of ibuprofen. Each hour, the amount of ibuprofen in the person’s system decreases by about 29%. How much ibuprofen is left after 6 hours?
51.24 mg of ibuprofen
Factor: x2 - 16x + 64
(x - 8)2
Identify the vertex by completing the square:
x2 + 10x + 5
(x + 10)2 - 20
Vertex: (-10, -20)
(4x + 3x2 + 15) - (5 + 7x - x2)
4x2 - 3x + 10
Solve the following quadratic equation by using the quadratic formula, then state if the roots are real or complex: 2x2 + 9x + 4 = 0
x=-1/2, x= -4
REAL
You buy a new computer for $2100. The value of the computer decreases by 20% annually. When will the computer have a value less than $600?
After 6 years when the value will be $550.50
3x2 - 10x - 8
(3x + 2)(x - 4)
Identify the vertex by completing the square:
2x2 - 8x + 13
2(x - 4)2 - 19
Vertex: (4, -19)
Simplify:
(2x - 6x3 + 12 + 3x2) - (7x2 + 9x - 4 + x3)
-7x3 - 4x2 - 7x + 16
Solve the following quadratic equation by using the quadratic formula, then state if the roots are real or complex:
3x2 + 2x + 4
x = (-2 pm 2isqrt(11))/6
OR
x = (-1 pm isqrt(11))/3
COMPLEX
The foundation of your house has about 1,200 termites. The termites grow at a rate of about 2.4% per day. How long until the number of termites doubles?
Approximately 30 years when the number of termites will be 2,444.