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determine the number of turning points and x-intercepts state whether a is less than zero or a is greater than zero and determine the minimum degree of the function in the graph all right so lets see we have turning points remember thats where the graph changes from increasing to decreasing or vice versa so I see for turning points x-intercepts I see one two three four I see five turning points now what we said was an N degree polynomial has at most n intercepts x-intercepts and n minus 1 turning points so kind of turning that around if you have n x-intercepts you can have at least a degree n polynomial and if you have n minus 1 turning points you can have at least an N degree polynomial so kind of adding 1 to the turning points or equaling the x-intercepts the minimum degree is 5 now focusing on the end behavior to figure out a so notice that as we move far to the left the function is going to positive infinity as we move far to the right the function is going to negative infinity