Some Review Problems for Intermediate Algebra Exam 4

1. Solve by completing the square.

2. For each equation (i) first find what types of solutions will be obtained using the discriminant,
then (ii) solve the equation using the quadratic formula . (Recall that you will need to memorize
each for Test 4!)

3. Find k so that the given quadratic equation will have just one real solution .

4. Find a quadratic equation that has the solutions.

(i.e., both solutions are -2)

5. A steel ball is tossed into the air upward at 10 feet per second from a building that is a feet
tall. The ball’s height h at time t is given by s = -16t2 +10t+a. (a) Find the time at which
the object hits the ground, depending on a (i.e., that is, where s = 0). (b) How long does it
take the object to hit the ground if the building is 100 ft high? Answer to the nearest tenth
of a second.

6. Find x- intercepts (if there are any), the y- intercept and the vertex (x = -b/2a — you will
be given this formula for the test ), then sketch a graph of the function .

7. Let and and find the following.

(a) f(-2)
(b) g(2)
(c) g(-3)
(d) The graphs of both functions.

8. For each function f, (i) sketch a graph of y = f(x), (ii) determine whether f -1 exists using
the HLT, (iii) determine whether the function is one-to-one, and if so, (iv) find an equation
for f -1.

9. Write each exponential equation in logarithmic form and each logarithmic equation in exponential

10. Expand each equation as much as possible.

11. Write as a single logarithm .

12. Solve for x in each equation

13. Graph the equation by first making a table of points for the (exponential) inverse

14. Find the value of x in each equation . Round any decimal answers to two decimal places.

15. Use the formula to find the pH of a solution with hydrogen ion concentration

16. Find for a solution with pH= 7.5.

17. Solve each equation for the unknown .

18. Use the change -of-base formula (I’ll provide this one:b) and a calculator to
each of the following; round answers to two decimal places . Then explain what it is
you’ve found in exponential form.

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