## Exam 3 - Study Guide

1. Find the extreme value of a quadratic function. See chapter 4 review, problems 7-14.
2. Determine the right hand and left hand behavior of a polynomial function. See chapter 4 review, problems 21 - 24.
3. Find a polynomial with integer coefficients which has the given zeros. See chapter 4 review, problems 55 -58.
4. Use Descartes' Rule of Signs to list the possible number of positive, negative, and complex roots of a polynomial function. See chapter 4 review, problems 59 - 68.
5. Use the Rational Root Theorem to list the possible rational roots of a polynomial function. See chapter 4 review, problems 59 - 68.
6. Find all real and complex roots of a polynomial function. See chapter 4 review, problems 59 - 68.
7. Find the domain of a function, and indicate any horizontal or vertical asymptotes. See chapter 5 review, problems 1-4.
8. Write the partial fraction decomposition for a rational expression. See chapter 5 review, problems 27 - 34.
9. Find the equation of the specified parabola. See chapter 5 review, problems 47 - 50.
10. Find the equation of the specified ellipse. See chapter 5 review, problems 51 - 54.
11. Find the equation of the specified hyperbola. See chapter 5 review, problems 55 -58.
12. Identify the conic section or degenerate case. Possible answers are: no graph, point, line, parallel lines, intersecting lines, parabola, circle, ellipse, hyperbola. There are nine parts and nine possible answers - this is matching. See chapter 5 review, problems 35 - 46, but this doesn't necessarily cover all the possibilities. The answers should be immediately apparent without the need to put into standard form.
13. Write a polynomial function with integer coefficients whose sketch is shown. Leave the polynomial in factored form.
14. Sketch the rational function given.
Where specific problems are given out of the review (with the exception of number 12), the problem on the test is one of those problems.