## Exam 3 - Study Guide

- Find the extreme value of a quadratic function. See chapter 4 review, problems 7-14.
- Determine the right hand and left hand behavior of a polynomial function. See chapter 4 review, problems 21 - 24.
- Find a polynomial with integer coefficients which has the given zeros. See chapter 4 review, problems 55 -58.
- 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.
- Use the Rational Root Theorem to list the possible rational roots of a polynomial function. See chapter 4 review, problems 59 - 68.
- Find all real and complex roots of a polynomial function. See chapter 4 review, problems 59 - 68.
- Find the domain of a function, and indicate any horizontal or vertical asymptotes. See chapter 5 review, problems 1-4.
- Write the partial fraction decomposition for a rational expression. See chapter 5 review, problems 27 - 34.
- Find the equation of the specified parabola. See chapter 5 review, problems 47 - 50.
- Find the equation of the specified ellipse. See chapter 5 review, problems 51 - 54.
- Find the equation of the specified hyperbola. See chapter 5 review, problems 55 -58.
- 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.
- Write a polynomial function with integer coefficients whose sketch is shown. Leave the polynomial in factored form.
- 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.