You can put this solution on YOUR website!
f(x) = ax^2 + bx + c
f(x-h) = a(x-h)^2 + b(x-h) + c
Simplifying. We start, of course, with the exponent. TO square (x-h) either use FOIL or the pattern
f(x-h) = a(x^2 -2(x)(h) + h^2) + b(x-h) + c
Now we multiply (using the Distributive Property):
f(x-h) = ax^2 - 2ahx + ah^2 + bx - bh + c
f(x-h) - f(x) = (ax^2 - 2ahx + ah^2 + bx - bh + c) - (ax^2 + bx + c)
Subtracting we get:
f(x-h) - f(x) = -2ahx + ah^2 - bh
Factoring out h in the numerator on the right side we get:
Now we can cancel the h's:
Since this did not work out as the problem says it should, it suggests that an error has been made. I do not think my work has an error. I believe the error is in the way you posted your problem. I believe you were supposed to find
If you rework the problem with (x+h), taking the same steps as above, you will end up with the correct answer.