# Equations and graphing

Please help with work and answers.

a) Calculate the value of the discriminant.

b) By examining the sign of the discriminant in part a, how many x-intercepts would the graph of have? Why?

6) a) Find the corresponding y values for x = -4, -3, -2, -1, 0, 1, 2 if .

b) Use Microsoft Excel to plot the points found in part a and to sketch the graph.

7) The path of a falling object is given by the function where represents the initial velocity in ft/sec and represents the initial height. The variable t is time in seconds, and s is the height of the object in feet.

a) If a rock is thrown upward with an initial velocity of 32 feet per second from the top of a 40-foot building, write the height equation using this information.

b) How high is the rock after 0.5 seconds?

c) After how many seconds will the rock reach maximum height?

d) What is the maximum height?

1) Solve the following algebraically. Trial and error is not an appropriate method of solution. You must show all your work.

a) 2x + 3 = 8

b) When graphed, this equation would be a line. By examining your answer to part a, what is the slope and y-intercept of this line?

Slope = ______

Y-intercept = _____

c) Using your answer from part a, find the corresponding value of y when x = 16.

3) The following graph shows Bob's salary from the year 2000 to the year 2003. He was hired in the year 2000; therefore, x = 0 represents the year 2000.

a) List the coordinates of two points on the graph in (x, y) form.

b) Find the slope of this line:

c) Find the equation of this line in slope-intercept form.

d) If Bob's salary trend continued, what would his salary be in the year 2005?

4) Suppose that the width of a rectangle is 5 inches shorter than the length and that the perimeter of the rectangle is 50.

a) Set up an equation for the perimeter involving only L, the length of the rectangle.

b) Solve this equation algebraically to find the length of the rectangle. Find the width as well.

5) A tennis club offers two payment options:

Option 1: $42 monthly fee plus $5/hour for court rental

Option 2: No monthly fee but $8.50/hour for court rental.

Let x = hours per month of court rental time.

a) Write a mathematical model representing the total monthly cost, C, in terms of x for the following:

Option 1: C=_________________

Option 2: C=_________________

b) How many hours would you have to rent the court so the monthly cost of option 1 is less than option 2? Set up an inequality and show your work algebraically using the information in part a. 

6) Plot the following points on the given rectangular coordinate system.

If you were to connect these points with a line, where would the y-intercept be located? Give the answer in (x, y) form.

#### Solution Summary

This provides examples of working with a variety of topics including discriminant of an equation, functions, graphing, and writing and solving equations.