Question 711569
That means, first Complete the Square.


Turn some of the function around some.
{{{f(x)=1-4x-x^2}}}
{{{f(x)=-x^2-4x+1}}}
Factor a negative 1 from the first two terms,
{{{f(x)=(-1)(x^2+4x)+1}}}


The quantity which will complete the square is {{{(4/2)^2=4}}}.
ADD and SUBTRACT 4, but add it inside the parentheses and subtract something related to it outside the parentheses.


{{{(-1)(x^2+4x+4)+1-(-1)(4)}}}
{{{-1(x^2+4x+4)+5}}}
{{{highlight(-1(x+2)^2+5)}}}, your standard form expression for your function f(x).