Linear Functions
Linear Regression
Quadratic Functions
Quadratic Word Problems
Inequalities
100
Find the slope and y-intercept of the following linear function:
y = -2/3x+5
m = -2/3; (0,5)
100
Is the following scatter plot linear or nonlinear? Explain.
linear; scatter plot creates linear slope
100
Graph the following function using transformations. Label all axes and three key points.
f(x) = (x + 2)^2 - 3
100
The price, in dollars, and the quantity x sold of a certain product obey the demand equation:
x = -5p + 100; 0<p<=20
Express the revenue R as a function of x. (Hint: R = xp)
R = -1/5x^2+20x
100
Using the graph below, find: g(x) < 0
x in (-oo, -1) U (4, oo)
200
Is the following relation linear or nonlinear? If it is linear, find the slope.
linear; m = 0.5
200
Given the table below, find the equation of the line of best fit (round to 4 decimal places).
y = -1.8x + 3.6
200
Graph the following function using transformations. Label all axes and three key points.
f(x) = -2x^2+4x
200
You have 2,000 feet of fencing to enclose a rectangular plot of land. What are the dimensions of the plot that produce maximum area? What is the maximum area?
500 ft by 500 ft; 250,000 sq. ft.
200
Using the graph below, find
f(x) >= g(x)
x in [-3, 1]
300
Is the following relation linear or nonlinear? If it is linear, find the slope.
linear; m = 0
300
Given the table below, find the equation of the line of best fit (round to 4 decimal places).
y = 0.4421x + 23.4559
300
For the function below, find: the coordinates of the vertex, the equation of the axis of symmetry, domain and range.
f(x) = -x^2 - 6x - 4
V(-3, 5); x = -3; x in (-oo, oo); y in (-oo, 5]
300
A parabolic arch has a span of 300 feet and a maximum height of 40 feet. Find the height of the arch 50 feet from the center.
33.6 feet
300
Solve the inequality and express using interval or set builder notation:
x^2 + 4 < 0
No real solutions
400
Find:
f(x) >= g(x)
x in [2,oo)
400
Predict the height of a child whose height is 26 inches tall using the equation for the line of best fit given the data table below. Round decimals to 2 places.
17.04 inches
400
Find an equation of a parabola whose vertex is (-2, -1) and contains the point (-3, 2).
y = 3(x+2)^2-1
400
Callaway Golf Company has determined that the marginal cost C of manufacturing x Big Bertha golf clubs may be expressed as the function below. How many clubs should be manufactured to minimize the marginal cost? At this level of production, what is the marginal cost?
C(x) = 4.9x^2-617.4x+19,600
63 clubs; $151.90
400
Solve the inequality and express using interval or set builder notation:
2x^2-5x-3 <= 0
x in [-1/2, 3]
500
Find:
g(x)<=f(x)<h(x)
x in [-6, 5)
500
Predict the height of a child whose head circumference is 17.4 inches using the equation for the line of best fit given the data table below. Round decimals to 3 places.
26.978 inches
500
Find the equation of the parabola below:
y = -1/4(x+4)^2 + 5
500
A track and field playing area is in the shape of a rectangle with semicircles at each end. The inside perimeter of the track is to be 1,500 meters. What should the dimensions of the rectangle be to maximize the area of the field?
750/pi m, 375 m
500
Solve the inequality and express using interval or set builder notation:
-4x^2+20x-25 < 0
x in (-oo, -5/2) U (-5/2, oo)