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MATH 112 Review for Test #3

1. Write the equation for the following parabola in Standard Form: y = x2 - 4x - 5.
a) Completing the Square Method :

 b) Vertex Method :

2. Write the equation for the following parabola in Standard Form: y = 4x2 - 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 = x2 - 9x + 18.

6. Find the x- intercept (s): y = x2 - 9x + 18.

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

7. Find the y-intercept(s):  y = x2 - 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) = x3 - 4x2 + 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) = ax and f(x) = ex ) 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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