# SOLUTION: How do I start this problem: Given f(x)=4+3x-x^2 ,find and simplify f(h+5) - f(h-3)

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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(15746)   (Show Source): You can put this solution on YOUR website!How do I start this problem: Here it is step-by-step : Given f(x)= 4 + 3x - x^2 , find and simplify f(h+5) - f(h-3) : f(h+5): substitute (h+3) for x in the equation: : 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 : 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 : Remember we had f(h+5) - f(h-3); therefore : (-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) : did this make sense to you?