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

Algebra ->  Polynomials-and-rational-expressions -> 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      Log On


   

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(39623) About Me  (Show Source):
You can put this solution on YOUR website!
y=-%28x-2%29%28x-5%29%5E2, just using the given zeros

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

graph%28300%2C300%2C-2%2C8%2C-5%2C5%2C-%28x-2%29%28x-5%29%5E2%29

Answer by greenestamps(13203) About Me  (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 P%28x%29+=+a%28x-2%29%28x-5%29%5E2

(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 P%28x%29+=+-%28x-2%29%28x-5%29%5E2

A graph...

graph%28400%2C400%2C-2%2C8%2C-20%2C20%2C-%28x-2%29%28x-5%29%5E2%29