Intermediate Algebra, Take Home Test 4
Quadratic, Exponential & Logarithmic Functions
Name: ______________________________ Student ID: _______________________
Instructions: Print this Take Home Test, and solve all problems using Blank Papers. You must show your work completely, and bring it on the day of the 4th on campus exam to get full credit.
Playback list to view the solutions to the practice test 4
| 1. Identify the Vertex: | a) | |
*Another solution to 1a | *Another solution to 1a | |
| b) | |
*Another solution to 1b | *Another solution to 1b |
*Video Lecture for Problems 1-9
2.
Find the x-intercept, the y-intercept, and the Vertex.
Determine whether the graph opens up or down. Find the Axis of
Symmetry and graph the function.
*Solution to problem 2 , *Another example for graphing prabola*(no audio)
3. What dimensions will yield the Maximum area for a rectangle of perimeter 60in?
4.
Determine the number of real solution(s) :
5. Solve by the square root property. *Video Lecture for more similar problems
a)
b) 
c) 
*Solution to similar problem to 5a
*Solution to similar problem to 5b
6. Solve by Completing the Square. Video Lecture for completing square method
| b) |  |
7. Solve by the Quadratic Formula: *Video Lecture on Problems 7a, 8a, 9, 15, 16, 2
a)
b) 
c)
*Another solutioin to problem 7a
*Another solution to problem 7b
*Another solution to problem 7c , *One more solution to problem 7c
8. Solve:
| a) |  |
||||
| b) |  |
||||
| c) |  |
*Solution to problem 8a
*Solution to problem 8b
*Another solution to problem 8c
9.
Solve by substitution.
*Another solution to problem 9
10.
Write a function that has the following solutions:
*Another solution to problem 10
11.
Solve and write the solution in interval
notation. 
12.
Solve and write the solution in interval
notation. 
*Another solution to problem 12
13. A model rocket will be launched from a hill 80 feet above the sea level. The launch site is next to the ocean (sea level), and the rocket will fall into the ocean. The rocket's distance, s, above sea level at any time, t, is found by the equation .
Find the time it takes for the rocket to strike the ocean.
14. Frank drove a distance of 300 miles one way; the round trip took him 11 hours. If he averaged 10 mph faster on his return trip, find his average speed going and returning.
*Another problem to problem 14
15. The base of a triangular sign is 5 feet less than three times the height. Find the base and height if the area of the triangle is 25 square feet.
*Another solution to problem 15
16. What is a one-to-one function?
*Another solution to problem 16
17. Find the inverse of the function,
 |
and find.
 |
18. Find the inverse of the function,*Video Lectures on Exponential, Logarithmic Functions, Applications, and Inverse Functions
 |
and find.
|
*Another solution to 18 , *Similar problem to 18
19. Graph * Video Lecture for Problem 19 and 21
 |
|
on the same set of axis and label important features.
*Another solution to 19 , *One more solution to problem 19,
20. Write each equation in logarithmic form.
a)
,
b) 
c) 
d) 
*Similar problem to 20a, *Another solution to 20a
*Another solution to 20b
*Another solution to 20c
*Another solution to 20d
21. Write each equation in exponential form.Video Lectures for Problems 21b, 22b, 26, 32
*Write as exponential form* (no audio)
a)
b) 
c) 
d) 
*Similar problem to 21a
*Another solution to 21b
*Another solution to 21c
*Solution 21d , *Similar problem to 21d,
22. Expand (Simplify) . a) b) c)
| a) |  |
*Another solution to 22a | ||||
| b) |  |
*Another solution to 22b | ||||
| c) |  |
*Another solutions to 22c | *Another example like Problem 22c | *Another example like problem 22c | ||
| *Solution to 22c | ||||||
23. Write as a single logarithm.
 |
24. Write as a single logarithm.
 |
*Solution to another problem like 24
25.
Solve. 
*Another solution to 25 , *Similar problem to problem 25
26.
Solve. 
27.
Solve. 
*Similar problem like problem 27
28.
Solve. 
*Similar problem like problem 28
*Lecture for Solving Exponential Equations
29. Solve and give EXACT answer for the following Exponential Equations.
a)
b) 
c) 
d)
e)
30. Assume ,
 |
evaluate
a)
b) 
*Solution 30b , *Another solution to 30b
31. Solve.
| a) |  |
| b) |  |
| c) |  |
*Another solution to 31C, *One more solution to 31C
32.
If Al invests $800 in a savings account earning interest at a rate of 6%
compounded semiannually, how long will it take for the $800 to grow to
$2,400? 
 |
*Solution to 32 , *Another solution to 32 *Another Example for Compound Interest Problem
33.PH= - 
where 
is the hydrogen ion concentration in moles/liter. Find the PH for the solution whose hydrogen ion concentration is 
, then classify as acid or base. *Solution 33 *
