SOLUTION: given f(x)= -x^3+2x^2-2x-2, find f(-2) and f(0)

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Question 107813: given f(x)= -x^3+2x^2-2x-2, find f(-2) and f(0)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Lets evaluate f%28-2%29

f%28x%29=-x%5E3%2B2x%5E2-2x-2 Start with the given polynomial


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


f%28-2%29=-%28-8%29%2B2%28-2%29%5E2-2%28-2%29-2 Evaluate %28-2%29%5E3 to get -8


f%28-2%29=-%28-8%29%2B2%284%29-2%28-2%29-2 Evaluate %28-2%29%5E2 to get 4

f%28-2%29=-%28-8%29%2B8-2%28-2%29-2 Multiply 2 and 4 to get 8

f%28-2%29=-%28-8%29%2B8%2B4-2 Multiply -2 and -2 to get 4

f%28-2%29=18 Now combine like terms


So when x=-2, f%28x%29=18


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Now lets evaluate f%280%29

f%28x%29=-x%5E3%2B2x%5E2-2x-2 Start with the given polynomial


f%280%29=-%280%29%5E3%2B2%280%29%5E2-2%280%29-2 Plug in x=0


f%280%29=-0%2B2%280%29%5E2-2%280%29-2 Evaluate %280%29%5E3 to get 0


f%280%29=-0%2B2%280%29-2%280%29-2 Evaluate %280%29%5E2 to get 0

f%280%29=0%2B0-2%280%29-2 Multiply 2 and 0 to get 0

f%280%29=0%2B0-0-2 Multiply -2 and 0 to get 0

f%280%29=-2 Now combine like terms


So when x=0, f%28x%29=-2