Question 715589
Standard form from general form comes by Completing the Square.  You ADD and SUBTRACT a square term.


{{{-(1/4)x^2+2x-2}}}
Factor the first two terms, {{{(-1/4)(x^2-8x)-2}}}
Identify the square term to use:  {{{(8/2)^2=16}}}...
Add and Subtract this square term, {{{(-1/4)(x^2-8x+16)-2-16*(-1/4)}}}  [did you understand what was done outside of the parentheses?]
Factor the square trinomial and do other arithmetic, {{{highlight(-(1/4)(x-4)^2+2)}}}


Function now in standard form, {{{highlight(f(x)=-(1/4)(x-4)^2+2)}}}