SOLUTION: Find f(-3) if f(x) = -2x^3-8x^2+2x-1

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Question 87258: Find f(-3) if f(x) = -2x^3-8x^2+2x-1
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=-2x%5E3-8x%5E2%2B2x-1 Start with the given polynomial


f%28-3%29=-2%28-3%29%5E3-8%28-3%29%5E2%2B2%28-3%29-1 Plug in x=-3


f%28-3%29=-2%28-27%29-8%28-3%29%5E2%2B2%28-3%29-1 Raise -3 to the third power to get -27


f%28-3%29=-2%28-27%29-8%289%29%2B2%28-3%29-1 Raise -3 to the second power to get 9


f%28-3%29=--54-8%289%29%2B2%28-3%29-1 Multiply 2 by -27 to get -54


f%28-3%29=--54-72%2B2%28-3%29-1 Multiply 8 by 9 to get 72


f%28-3%29=--54-72%2B-6-1 Multiply 2 by -3 to get -6


f%28-3%29=-25 Now combine like terms

Notice if we graph f%28x%29=-2x%5E3-8x%5E2%2B2x-1 and the point (-3,-25) we get

+drawing%28900%2C+900%2C+-10%2C+5%2C+-30%2C+5%2C%0D%0Agraph%28+900%2C+900%2C+-10%2C+5%2C+-30%2C+5%2C+-2x%5E3-8x%5E2%2B2x-1%29%2C%0D%0Acircle%28-3%2C-25%2C0.05%29%2C%0D%0Acircle%28-3%2C-25%2C0.08%29%29+

and we can see that (-3,-25) is on the curve. So this verifies our answer