Polynomials & Equations
Add the polynomials:
(7x2 + 6x - 9) + (2x2 - 4x)
5x2 + 2x - 9
Name the slope and the y-intercept.
y = -2x + 6
m = -2
y-intercept = 6
What type of vertex does the following equation have and how do you know?
y = -2x2 + 4x - 5
Maximum because the a value is negative which makes the graph facing down
Find f(3) when F(x) = 2x+1
f(3) = 9
Name the type of function:
1. y = 6x2 + 2x - 1
2. 4x + 5y = 10
3. y = 2x + 6
1. Quadratic
2. Linear
3. Exponential
Subtract the polynomials:
(8x2 + 6x) - (3x2 - 3x + 2)
5x2 + 9x - 2
What is the domain and range of all linear functions that are not real-world applications?
Domain: ARN
Range: ARN
Factor out the GCF of 5x2 + 10x - 15
5(x2 + 2x - 3)
Does this equation show growth or decay and how do you know?
y = 4(0.5)x
Decay because the b value is between 0 and 1
Solve the systems of equation:
y = 2x
3x + y = 10
Write your answer as an ordered pair.
(2, 4)
Solve for x.
3(2x + 6) = 24
x = 1
Find f(9) using the equation f(x) = 2x + 1
f(9) = 19
Factor: 9x2 - 25
(3x - 5)(3x + 5)
If Todd invested shown in the exponential equation below, how much money will he have after 6 years?
y = 2(1.5)t
y = $22.78
Is the following sequence an arithmetic or geometric sequence and how do you know?
6, 9, 12, 15....
Arithmetic because you are adding 3 each time
Multiply the binomial.
(3x + 1)(5x + 4)
15x2 + 17x + 4
Find the rate of change when x = 2 and x = 6 using the equation:
y = -4x + 1
m = -4
Find the zeros or roots.
y = 2x2 + 7x + 3
Hint: Factor and solve OR use the quadratic formula.
x = -3 and x = -1/2
Find the rate of change at the interval [0, 2] when y = 3x
m = 4
Name the vertex from the following equation and state if the graph has a maximum or a minimum.
y = (x + 7)2 + 3
(-7, 3)
minimum
If the length of a rectangular garden is (4x + 2) and the width is (2x + 1), find the area of the rectangle.
Hint: Area = length x width
8x2 + 8x + 2
Find the x-intercept and y-intercept using the following equation:
y = 2x + 8
x-intercept = -4
y-intercept = 8
A rocket has just launched and we want to find out it's maximum value using the equation:
y = -2x2 + 4x + 1
Vertex: (1, 3)
maximum value = 3
You start with $200 and invest at a rate of 25%. Write an equation to represent this situation.
How much will you have after 5 years?
y = 200(1.25)x
y = $610.35
Which is a solution set to the equation 2x - 3y = 13
a. (5, -1)
b. (2, 3)
c. (5, 6)
d. (-1, 5)
A