# MATH 112 Review for Test #3

1. Write the equation for the following parabola in
Standard Form: y = x^{2} - 4x - 5.

a) Completing the Square Method :

b) Vertex Method :

2. Write the equation for the following parabola in
Standard Form: y = 4x^{2} - 4x + 21.

a) Completing the Square Method :

b) Vertex Method:

3. Write the equation for the following parabola in
Standard Form:

a) Completing the Square Method:

b) Vertex Method:

4. Graph the function : f (x) = (x +1)^{2} − 2.

5. Find the vertex of the following parabola: y = x^{2} - 9x + 18.

6. Find the x- intercept (s): y = x^{2} - 9x + 18.

x-intercepts:(6 ,0) and (3,0)

7. Find the y-intercept(s): y = x^{2} - 9x + 18.

y = (0)^{2} - 9(0) + 18 = 0 + 18 = 18

y-intercept: (0,8)

8. Find all real zeros of the function: f(x) = x^{3} - 4x^{2}
+ 4x .

9. Use long division to divide , factor and find all zeros.

a) Divide by long division:

b) Use results from the above long division to factor the dividend
completely.

c) Use results from the above factorization to find all
zeros of the dividend .

10. Divide by synthetic division :

put in decreasing order by powers , with any placeholders, first:

11. Find all vertical asymptote(s):

12. Find all horizontal asymptote(s):

highest power in numerator = 1; highest power in denominator = 1

highest power in numerator = highest power in denominator

so

y = -5/2

13. Find all horizontal asymptote(s):

highest power in numerator = 2; highest power in denominator = 1

highest power in numerator > highest power in denominator

so no horizontal asymptote

14. Find any slant asymptote(s):

highest power in numerator = highest power in denominator +1, so there is a
slant asymptote

15. Be able to recognize the graphs of exponential functions (f(x) = a^{x} and f(x)
= e^{x} ) and logarithmic

functions (f(x) =
and
lnx ). Also, be able to recognize each of their translations and reflection

Examples of a few of these are shown below. See your
textbook for more.

16. Evaluate each of the following logarithms.

17. Evaluate each of the following for x.

18. Convert each of the following from exponential form to
logarithmic form.

19. Convert each of the following from logarithmic form to
exponential form.

21. Use a calculator and the change of base formula to
evaluate:

22. Use a calculator to evaluate the following. Round to
the nearest thousandth.

23. Expand each of the following logarithms.

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