1. Notes P.6 – Solving Inequalities

2. I. Absolute Values:
A. If | u | < a, then u is in the interval (-a, a).
B. If | u | > a, then u is in the interval (-∞, -a) or (a, ∞).

3. C. Solve the following both algebraically and graphically:

4. Graphically: See TI-83+ Overhead.

5. II. Solving Quadratic Inequalities:
A. Ex- Solving
Algebraically - We will use a function sign test, i. e., we will check the sign of the function in the intervals between the zeroes of the function

6. Factor to get
The expression on the left is equivalent to zero at x = -2 and x = 5. We will therefore check the SIGN of the expression in the intervals (-∞,-2), (-2, 5) and (5, ∞) for our solution.

7. _ + +

8. Graphically: See TI-83+ Overhead.

9. III. Cubics, Quartics, etc:
A. Algebraically – Factor and use the sign test.
B. Graphically if unfactorable.

10. IV. Projectile Motion: A. Vertical – Straight up and/or down
B. Units –
1.) In feet –
2.) in meters -
Initial Velocity
Initial Position

11. V. Quick Review
1. ) Solve
2.) Solve by using the sign test and confirming graphically.
3.) Solve by using the sign test and confirming graphically.

12. Quick Review cont. 4. ) Solve
5.) A projectile is launched from a height of 16 ft. above ground with an initial velocity of 256 ft./sec. Determine when the projectile reaches a height of 128 ft.

13. Homework: p.52 #3,7,11,15,19,23,27,31,35,39,43,45-51