The powers are in descending order. The largest power on x. Should be first term. nth degree vertices LHB RHB How many times an x-int repeats.

Notice the right hand side doesn’t change Where the y-coordinates are going to a > 0, positive value a > 0, positive value Notice the right hand side doesn’t change LHB RHB LHB RHB a < 0, negative value a < 0, negative value 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 1. Most turning points n – 1 = 6 – 1 = 5 2. Possible turning points, 4, 2, 0 2. Possible turning points, 5, 3, 1

y = x y = x 1 1 1 1 y = x5 y = x3 -1 1 -1 -1 1 1 -1 1 -1 -1 -1 -1 Odd multiplicity always crosses the x-axis. Even multiplicity always does a “Touch & Go”. Never crosses the x-axis.

x * x2 = -2 * (+1)2 = Turning Pts = 2 or 0 The graph will have end behavior like the graph x3. Y-intercept at (0, -2). Occurs twice, Multiplicity of 2 (-1, 0) 2 (2, 0) 1 Graph in your calculator to find relative max and min for intervals of increasing and decreasing. (0, -2)

+ 0 Turning Pts = 3 or 1 Not a constant The graph will have end behavior like the graph -0.2x4. Y-intercept at (0, 0). Occurs twice, Multiplicity of 2 (-2, 0) 1 (4, 0) 1 (0, 0) 2 Graph in your calculator to find relative max and min for intervals of increasing and decreasing.

Factor by grouping Turning Pts = 2 or 0 The graph will have end behavior like the graph x3. Y-intercept at (0, -12). (-3, 0) 1 (-2, 0) 1 (2, 0) 1 Graph in your calculator to find relative max and min for intervals of increasing and decreasing. (0, -12)

FOIL conjugate pair. FOIL again.

FOIL. Distribute.