## Math 098 - Chapter 9-10 Study Guide

1. Solve the quadratic equation using any algebraic technique. Algebraic techniques include factoring, extraction of roots, completing the square, and the quadratic formula. Seven parts (6 from 9.3 and 1 from 9.4). Look at problems 9.3.27 - 9.3.51 and 9.4.3 - 9.4.13.
2. Solve the inequality. Write the answer in interval notation. Two parts. Look at problems 9.6.23 - 9.6.29 and 9.6.49 - 9.6.63.
3. Consider a quadratic function. Sketch the graph of the function. Find the domain and range of the function. Find the x-intercepts (if any) and the y-intercept. Find the vertex and the axis of symmetry. Look at problems 9.8.73 - 9.8.77.
4. Determine the center and radius of the given relation. Look at problems 10.2.25 - 10.2.33.
5. Sketch the graph of the given equation. Look at problems 10.2.51 - 10.2.63.
6. Determine the center and radius of the circle. Look at problems 10.2.65 - 10.2.77.
7. Use the discriminant to determine the number and nature of the solutions of the given equation. Two parts. Look at problems 9.3.55 - 9.3.61.
8. Write a quadratic equation with integer coefficients that has the given pair of numbers as solutions. Look at problems 9.1.79 - 9.1.85.
9. Solve the quadratic equation by factoring. Look at problems 9.1.17 - 9.1.25.
10. Solve the quadratic equation by extraction of roots. Look at problems 9.1.29 - 9.1.36.
11. Solve the quadratic equation by completing the square. Look at problems 9.2.31 - 9.2.37.
12. Solve the quadratic equation by the quadratic formula. Look at problems 9.3.17 - 9.3.23.

### Notes:

• All of the problems are directly from the textbook.
• In problem 1, you are free to use whichever technique you want to.
• Problems 9-12 request that you solve the problem using a particular technique. 2 of the points are for using the correct technique, 3 of the points are for obtaining the correct solution. So, if you cannot use that technique, go ahead and solve the problem using some other technique for some of the credit.
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