1. The powers are in descending order. The largest power on x. Should be first term. n th degree vertices How many times an x-int repeats. LHBRHB

2. LHBRHB a > 0, positive value a < 0, negative value LHBRHB a > 0, positive value a < 0, negative value Notice the right hand side doesn’t change Two concepts that we need to know about turning points. 1. The most turning points a polynomial function can have is n – 1. 2. Turning points can reduce by 2 only, until it reaches a 1 or 0. - this is based on odd multiplicity of 3 or higher. Example. 1. Most turning points n – 1 = 5 – 1 = 4 2. Possible turning points, 4, 2, 0 1. Most turning points n – 1 = 6 – 1 = 5 2. Possible turning points, 5, 3, 1

3. 1 1 1 1 y = x 1 1 1 1 y = x y = x 3 y = x 5 Even multiplicity always does a “Touch & Go”. Never crosses the x- axis. Odd multiplicity always crosses the x-axis.

4. x * x 2 = -2 * (+1) 2 = (0, -2) (2, 0) 1 (-1, 0) 2 Turning Pts = 2 or 0 Occurs twice, Multiplicity of 2 Graph in your calculator to find relative max and min for intervals of increasing and decreasing.

5. Turning Pts = 3 or 1 + 0 Occurs twice, Multiplicity of 2 (-2, 0) 1 (0, 0) 2 (4, 0) 1 Graph in your calculator to find relative max and min for intervals of increasing and decreasing. Not a constant

6. Turning Pts = 2 or 0 (2, 0) 1 (-3, 0) 1 (-2, 0) 1 (0, -12) Factor by grouping Graph in your calculator to find relative max and min for intervals of increasing and decreasing.

7. FOIL conjugate pair. FOIL again.

8. FOIL. Distribute.