You can
put this solution on YOUR website!
f(x) = -x²-4x-7
Factor -1 out of the first two terms on the right.
f(x) = -1(x²+4x)-7
Complete the square inside the parentheses:
1. Multiply the coefficient of x by 
. 4· = 2
2. Then square that, get 4
3. Add then subtract 4 inside the parentheses. That
is, add +4-4 which does not affect anything since
4-4 is just 0. Also change the parentheses to
brackets so they can hold parentheses:
f(x) = -1[x²+4x+4-4]-7
Group the first three terms inside the bracket in a
parentheses:
f(x) = -1[(x²+4x+4)-4]-7
Factor that trinomial (x²+4x+4) as
(x+2)(x+2) or (x+2)²
f(x) = -1[(x+2)²-4]-7
Next we remove the bracket by distributing the -1
into the bracket. The -1 first multiplies by the
(x+2)² leaving it intact as -1(x+2)². Then the -1
also multiplies by the -4 in the bracket and gives
+4. So we have this:
f(x) = -1(x+2)²+4-7
and finally:
f(x) = -1(x+2)²-3
Edwin
