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First remember these:
f(x) = ax²+bx+c,
where a, b and c are real numbers and a≠0 <<< quadratic function
f(x)= a(x-h)²+k <<<< standard or the vertex form
example this is the given f(x)= -x²+50x 
1.)  first factor out a in f(x) = ax²+bx+c , in this case a=-1 therefore the equation is now f(x)=-(x²-50x) 
2.) make the expression inside the parenthesis a perfect square trinomial by adding (1/2·b/a)², then subtract the correspond value of a (1/2·b/a)². we did that so the value of the expression would not change because we added 0. hence,
  f(x)= -(x² - 50x + 625)- (-625)
       = -(x² - 50x + 625) +625
3.) we'll factor the perfect square trinomial.
   f(x)= -(x - 25)²+625
x is now in the standard form 
where a=-1, h=25 and k=625

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