Polynomial Operations
Solving Quadratics
Vertex + Transformations of Quadratics
Graphical Features
Simplifying Radicals / Exponential Functions
100
Add the polynomials and simplify:
(4x2+2x-10)+(3x2-5x+3)
7x2-3x-7
100
Factor the following quadratic:
x2+6x+5
(x+5)(x+1)
100
What is the vertex:
f(x)=2(x-6)2+7
(6,7)
100
Does this function have an asymptote or a break? Where is it?
f(x)=(x-3)/(x-4)
Asymptote at x = 4
100
sqrt(63)
+-3sqrt7
200
Subtract the polynomials and simplify
(4x3+7x2+2x)-(x2-9x+15)
4x3+6x2+11x-15
200
Factor: 3x2 -25x +8
(3x-1)(x-8)
200
f(x)=2(x+9)2-4
(-9,-4)
200
Does this function have an asymptote or a break? Where is it?
g(x)=(3(x+2))/(x+2)
A break at x = -2
200
sqrt(-16)
+-4i
300
Subtract the polynomials and simplify
(7x2+2x+12)-(3x2+5x-10)
4x2-3x+22
300
Solve using the quadratic formula:
3x^2+5x-7=0
x=(-5+sqrt109)/6 OR (-5-sqrt109)/6
300
What is the vertex?
(4,2)
300
Domain: (-infinity, 2) U (2,infinity)
Range: (-infinity,0) U (0,ifinity)
300
Write an exponential equation for this scenario:
In January, you had 80 points in Algebra II. You started coming to tutoring and your grade started increasing at a constant ratio of 1.02 (2% a month).
f(x)=80(1.02)^x
400
Multiply and simplify:
(2x+7)(7x-5)
14x2+39x-35
400
Solve the quadratic equation using your method of choice:
u^2-5u-14=0
u= _____ or _____
u=-2 or 7
400
How does the graph of the quadratic change with the transformation?
Original: Transformed:
f(x)=1(x-0)2+0 f(x)=2(x-5)2-1
Fill in the blank and select the direction (up/down)
The graph moved _____ (up/down)
The graph moved 1 down
400
As x -> infinity, y ->0
As x -> -infinity, y ->0
400
Write an exponential function for the scenario:
p(m) = 267(1.042)m
500
A table has a width of 6x+3 inches and length 2x-7 inches. What is the area of the picture? The table is a rectangle.
12x2-36x-21
500
Solve using the quadratic formula
2x2 - 5x - 12 = 0
x = 4 or -3/2
500
How does the graph of the quadratic change with the transformation?
Original: Transformed:
f(x)=1(x-0)2+0 f(x)=2(x-5)2-1
Fill in the blank and select the direction (left/right)
The graph moved _____ (left/right)
The graph moved 5 right.
500
Approximate your answer! (As close as you can)
(0,0)
or (0,-1/5)
500
Write an exponential equation for this scenario:
The House Problem:
A house is purchased for $400,000 in 2026. The value of the house depreciates at a rate of 10%.
f(x)= ________________________ (5 pts)
f(x)=400,000(0.9)^x