Question 825023
This relies on Completing the Square.  This kind of question happens often.


Factor the -4 from the entire right-hand expression:
{{{h(x)=-4(x^2+2x-3/4)}}}
The terms containing x in the quadratic expression in the parentheses represents a square with the area {{{(2/2)^2=1}}} missing.  We ADD and SUBTRACT this inside the parentheses.
{{{h(x)=-4(x^2+2x+1-3/4-1)}}};
{{{h(x)=-4((x+1)^2-3/4-1)}}}
{{{h(x)=-4((x+1)^2-7/4)}}}
Remultiply the -4:
{{{highlight(h(x)=-4(x+1)^2-7)}}}