SOLUTION: HElp f(x)=-2x(cubed)+5x(squared)-x-1 find (a)f(-1), (b)f(0), and (c)f(2) thanks Heather

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Question 110902: HElp
f(x)=-2x(cubed)+5x(squared)-x-1
find (a)f(-1), (b)f(0), and (c)f(2)
thanks
Heather
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Lets evaluate f%28-1%29

f%28x%29=-2x%5E3%2B5x%5E2-x-1 Start with the given polynomial


f%28-1%29=-2%28-1%29%5E3%2B5%28-1%29%5E2-%28-1%29-1 Plug in x=-1


f%28-1%29=-2%28-1%29%2B5%28-1%29%5E2-%28-1%29-1 Evaluate %28-1%29%5E3 to get -1


f%28-1%29=-2%28-1%29%2B5%281%29-%28-1%29-1 Evaluate %28-1%29%5E2 to get 1

f%28-1%29=%2B2%2B5%281%29-%28-1%29-1 Multiply -2 and -1 to get 2

f%28-1%29=%2B2%2B5-%28-1%29-1 Multiply 5 and 1 to get 5

f%28-1%29=7 Now combine like terms


So when x=-1, f%28x%29=7






Lets evaluate f%280%29

f%28x%29=-2x%5E3%2B5x%5E2-x-1 Start with the given polynomial


f%280%29=-2%280%29%5E3%2B5%280%29%5E2-%280%29-1 Plug in x=0


f%280%29=-2%280%29%2B5%280%29%5E2-0-1 Evaluate -2%280%29%5E3 to get 0


f%280%29=-2%280%29%2B5%280%29-0-1 Evaluate 5%280%29%5E2 to get 0

f%280%29=0%2B5%280%29-0-1 Multiply -2 and 0 to get 0

f%280%29=0%2B0-0-1 Multiply 5 and 0 to get 0

f%280%29=-1 Now combine like terms









Lets evaluate f%282%29

f%28x%29=-2x%5E3%2B5x%5E2-x-1 Start with the given polynomial


f%282%29=-2%282%29%5E3%2B5%282%29%5E2-%282%29-1 Plug in x=2


f%282%29=-2%288%29%2B5%282%29%5E2-2-1 Evaluate %282%29%5E3 to get 8


f%282%29=-2%288%29%2B5%284%29-2-1 Evaluate %282%29%5E2 to get 4

f%282%29=-16%2B5%284%29-2-1 Multiply -2 and 8 to get -16

f%282%29=-16%2B20-2-1 Multiply 5 and 4 to get 20

f%282%29=1 Now combine like terms