Question 955134: Sketch a cubic function(third degree polynomial function) y=p(x) where p(x)>0 on the intervals (5,8) and (-∞,-3). Also determine the formula.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! The roots are 5, 8, and -3
So the factors are (x-5), (x-8), (x+3)
Multiply everything out
(x-5)(x-8)(x+3)
(x-5)(x^2-5x-24)
x(x^2-5x-24)-5(x^2-5x-24)
x^3-5x^2-24x-5x^2+25x+120
x^3-10x^2+x+120
Let's see what the graph looks like
that's the opposite of what we want, so simply flip it over the x axis to get
Algebraically, you are multiplying EVERY term by -1 so
x^3-10x^2+x+120 turns into -x^3+10x^2-x-120
The final answer is y = -x^3+10x^2-x-120
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