Question 34931
{{{ f(x)=x^2-2x-7 }}}


Things like this are nice and straight forward:
{{{ f(a-1)=(a-1)^2-2(a-1)-7 }}}
{{{ f(a-1)=a^2-4a-4 }}}


{{{ f(a+h)=(a+h)^2-2(a+h)-7 }}}
{{{ f(a+h)=a^2+2ah+h^2-2a-2h-7 }}}


and {{{ f(a)=a^2-2a-7 }}}


So, {{{ f(a+h) - f(a) = a^2+2ah+h^2-2a-2h-7 - (a^2-2a-7) }}}
{{{ f(a+h) - f(a) = a^2+2ah+h^2-2a-2h-7 -a^2+2a+7 }}}
{{{ f(a+h) - f(a) = 2ah+h^2-2h }}}
{{{ f(a+h) - f(a) = h^2+2ah-2h }}}


jon.