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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

steps:

example this is the given f(x)= -x²+50x

1.) first factor out a in

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

f(x)=a(x-h)²+k

where a=-1, h=25 and k=625