Math 110                                                                                               Name: ______________________________

Exam IV: part 5.1, 5.2 – 5.6, part 6.0                                   Date:   ______________________________

Directions: Show all work to get full credit. Total points possible = 30pts. Each point is worth 3.33%.

Part I:  Only scientific calculators allowed.

1.          (2 pts) Find the quadratic equation for the parabola below. Assume the ‘a’ value is 1.

Note: Pay attention to the scaling.

                                   Equation: __________________________

2.          (3 pts) Simplify:   

3.          (3 pts) Determine the quotient using long division:      

4.          (3 pts) Solve:               Hint: It is a proportion!

5.          (3 pts) Simplify: 

6.          (4 pts) Solve and check solutions:                   

7.        (3 pts) A landfill will be in service 10 years if each of the 50,000 households throws away a full 90-gallon container per week. If the same households recycle and reduce the throw-away portion to 30 gallons per week, how long will the landfill be in service?

Note: Assume the number of years the landfill will be in service is inversely proportional to the number of gallons of trash produced per week.  Remember to use algebra to justify your answer and clearly identify your variables.

8.     (3 pts)  Inspect the table and answer parts ‘a’ and ‘b’:

a.        Does the table represent direct or inverse variation? Justify/explain your answer.

b.       What is value of k, the constant of proportionality?

Name      ___________________________

Part II:  Graphing calculators allowed.

9.    (3 pts) Give all the information below about the graph of the basic rational function .

Domain:                                                                         ______________________________                   

x-intercept point(s):                                                     ______________________________

y-intercept point(s):                                                     ______________________________

where the function is increasing:                                              ______________________________

where the function is decreasing:                       _______________________

equation of horizontal asymptote                              _______________________

10.   (3 pts)  A happy San Diego Charger fan throws a football vertically into the air with an initial velocity of 15 ft/sec. Assume the ball leaves the fan’s hand at a height of 6.5 ft. Let g = 32.2 ft/sec².

a.        Write the simplified equation representing the height the football is off the ground as a function of

        time. Use the vertical motion formula:  

b.       What is the maximum height the football is from the ground? When does this occur?