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. Please show your work completely, and post them in the discussion forum on Canvas befoer the due date.
| 1. Identify the Vertex: | a) | |
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| b) | |
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.
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.
a)
b) 
c) 
6. Solve by Completing the Square.
| b) |  |
7. Solve by the Quadratic Formula:
8. Solve:
| a) |  |
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| b) |  |
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| c) |  |
9.
Solve by substitution.
10.
Write a function that has the following solutions:
11.
Solve and write the solution in interval
notation. 
12.
Solve and write the solution in interval
notation. 
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.
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.
16. What is a one-to-one function?
17. Find the inverse of the function,
 |
and find.
 |
18. Find the inverse of the function,
 |
and find.
|
19. Graph
 |
|
on the same set of axis and label important features.
20. Write each equation in logarithmic form.
a)
,
b) 
c) 
d) 
21. Write each equation in exponential form.
a)
b) 
c) 
d) 
22. Expand (Simplify) . a) b) c)
| a) |  |
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| b) |  |
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| c) |  |
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23. Write as a single logarithm.
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24. Write as a single logarithm.
 |
25.
Solve. 
26.
Solve. 
27.
Solve. 
28.
Solve. 
29. Solve and give EXACT answer for the following Exponential Equations.
a)
b) 
c) 
d)
e)
30. Assume ,
 |
evaluate
a)
b) 
31. Solve.
| a) |  |
| b) |  |
| c) |  |
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? 
 |
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.
b) 
c)
