SOLUTION: Write an equation for a cubic polynomial p(x) with leading coefficient -1 whose graph passes through the point (2, 8) and is tangent to the x-axis at the origin.

Question 707573: Write an equation for a cubic polynomial p(x) with leading coefficient -1 whose graph passes through the point (2, 8) and is tangent to the x-axis at the origin.
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!

derivative of p(0) must be zero because of tangent at the origin. Taking derivative, setting it equal zero, seems c=0.

p(2)=8, so carrying this through did not seem to help. 8=-8+4b+d, not too useful.

Point (0,0) must satisfy our p(x) polynomial, so ,
apparantly d=0.

So far we seem to have .
Let's try point (2,8) again.
, also.
Using the point,
.
b=4

THIS should work well:
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