1. November 1 st copyright2009merrydavidson Warm Up 1) Complete the Square to change to Standard Form. f(x) = 2x 2 – 8x + 9 2)Find ALL roots using the rational root theorem, factoring and/or quadratic formula. f(x) = x 4 + 3x 3 – 5x 2 - 21x + 22 y = 2(x – 2) 2 + 1

2. Polynomial Inequalities x 3 + 3x 2 – x – 3 < 0 dashed Where is the polynomial less than 0?

3. Let’s do this without having to graph it first.

4. Polynomial Inequalities x 3 + 3x 2 – x – 3 < 0 Step 1: Find the CRITICAL numbers. Solutions are critical numbers so solve for x =. x = + 1, -3 Since it is “<“ and not “<‘; place on the x-axis as a hole.

5. x 3 + 3x 2 – x – 3 < 0 Step 2:Test a point on each interval in the original inequality to see if it is “true” or “false”. The solution is the intervals that turn out TRUE. -3 -1 1 FT F T

6. Process for solving polynomial inequalities…… Pretend it is equal to zero and find zero’s Put those on the number line closed circles open circles Test sections into the ORIGINAL inequality for T or F Write the answer in interval notation for the true sections

7. You do this one…… 2x 3 – 3x 2 – 32x > - 48

8. Rational inequalities Find the solution to a rational inequality algebraically.

9. Solve rational inequalities Step 1: Rewrite fractions with factored denominator Step 2: Find domain restrictions. Put this number on a number line as a “hole”. Step 3. pretend it is = 0 and find the zero’s. Put this value on the number line as open or closed circles. closed circles open circles Already done (x-2) x + 4 = 0 x = -4 2-4

10. Solve rational inequalities -4 2 Step 4: Test intervals using the original inequality. Step 5. Write the solution in interval notation. TF T

11. Process for solving rational inequalities…… Find domain restrictions from the denominator and put a hole on the number line Pretend it is equal to zero and find zero’s Put those on the number line as open/closed dots Test sections into the ORIGINAL inequality for T or F Write the answer in interval notation for the true sections A common mistake is to forget to do the first step!

12. You do this one……

15. Quiz next time over…. Find critical numbers for inequalities Solve polynomial and rational inequalities Graph a rational function including intercepts, asymptotes and correct end behavior Function composition Evaluating a function for a specific value

16. HW: WS 4-5