Area Problems
Equations
Graph Characteristics
Transformations
100
A home improvement show is designing a backyard for a family. They want to install a pool in the center of the backyard. It will have two equal square sections of garden on both sides of it. The entire length of the backyard is 60 feet. Let p represent the width of each square section of garden.
Draw a picture to represent this scenario, labeling the sides of the pool.
[depends]
100
Determine the AOS and concavity of the function
f(x) = -2x^2-3x+4
x = -0.75
concave down
100
Determine the y-intercept and x-intercepts.
yint (0,0)
xints (-2, 0) and (0,0)
100
Describe the transformations for the function
f(x) = x^2 +5
move up 5
200
A home improvement show is designing a backyard for a family. They want to install a pool in the center of the backyard. It will have two equal square sections of garden on both sides of it. The entire length of the backyard is 60 feet. Let p represent the width of each square section of garden.
Write an expression to represent the length of the pool.
l = 60 -2p
200
Determine the vertex of the function
f(x) = 2x^2+8x-5
Does it have a minimum or maximum?
(-2, -13)
min
200
Determine the vertex and axis of symmetry. 
V (-1, 2)
AOS x = -1
200
Describe the transformations for the function
f(x) = -x^2-4
reflected across x axis, shifted down 4
300
A home improvement show is designing a backyard for a family. They want to install a pool in the center of the backyard. It will have two equal square sections of garden on both sides of it. The entire length of the backyard is 60 feet. Let p represent the width of each square section of garden.
Write a function A(p) to represent the area of the pool as a function of the width, p, of each square section.
a(p) = p(60-2p)
300
Determine the vertex of the function. What are the zeros?
f(x) = 2(x-3)(x-7)
(5,-8)
Zeros x = 3, 7
300
Determine the intervals of increase and decrease.
Inc (-oo, -1)
Dec (1, oo)
300
Describe the transformations for the function
f(x) = 1/3(x-1)^2
shrink by a factor of 1/3, shifted right by 1
400
Using Desmos, determine the absolute minimum or maximum of the area equation. Describe what it means in the context of the problem.
(15, 450)
a pool width of 15 gives a max area of 450 ft
400
Determine the vertex of the function. Does it have a min or max?
f(x) = -(x+3)^2-2
V (-3, -2)
Max
400
Determine domain and range. 
D: (-oo, oo)
R: (-oo, 2]
400
Describe the transformations for the function
f(x) = -4(x+3)-7
reflected across x axis, stretched by a factor of 4, shifted left by 3, shifted down 7