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Question 81250: How do I start this problem:
Given f(x)=4+3x-x^2 ,find and simplify f(h+5) - f(h-3)
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! How do I start this problem:
Here it is step-by-step
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Given f(x)= 4 + 3x - x^2 , find and simplify f(h+5) - f(h-3)
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f(h+5): substitute (h+3) for x in the equation:
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f(h+5) = 4 + 3(h+5) - (h+5)^2
f(h+3) = 4 + 3h + 15 - (h^2 + 10h + 25): FOILed the square
f(h+3) = 4 + 3h + 15 - h^2 - 10h - 25; Removing the brackets, changes the signs
f(h+3) = -h^2 + 3h - 10h + 4 + 15 - 25
f(h+3) = -h^2 - 7h - 6
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Do the same with (h-3)
f(h-3) = 4 + 3(h-3) - (h-3)^2
f(h-3) = 4 + 3h - 9 - (h^2 - 6h + 9)
f(h-3) = 4 + 3h - 9 - h^2 + 6h - 9
f(h-3) = -h^2 + 3h + 6h + 4 - 9 - 9
f(h-3) = -h^2 + 9h - 14
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Remember we had f(h+5) - f(h-3); therefore
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(-h^2 - 7h - 6) - (-h^2 + 9h - 14)
-h^2 - 7h - 6 + h^2 - 9h + 14; note the change in signs here
- h^2 + h^2 - 7h - 9h - 6 + 14
Therefore we have:
f(h+5) - f(h-3) = (-16h + 8)
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did this make sense to you?
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