SOLUTION: sketch a cubic function (third degree polynomial function y=p(x) with two distinct zeros at x=2 and x=5 and has a local maximum located at x=5 then determine a formula for your fun

Question 1113425: sketch a cubic function (third degree polynomial function y=p(x) with two distinct zeros at x=2 and x=5 and has a local maximum located at x=5 then determine a formula for your function. [Hint you will have one double zero]
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39625) (Show Source): You can put this solution on YOUR website!
, just using the given zeros

Observe the negative sign, to make the needed local MAXIMUM.

Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

(1) The hint is not really needed; if a cubic function has exactly two distinct zeros, then one of them is a double root.

(2) Since there is a local maximum at one of the roots, the double root must be at that root.

So the equation is of the form

(3) Since the double root is the larger root, and since the function has a local minimum there, the coefficient a must be negative.

There is no information given that tells us what that coefficient is, so we can choose any negative number. -1 is easiest. So a function that satisfies the given requirements is

A graph...

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