Question 140379
{{{g(x)=-x^2-3x}}}
For any quadratic equation of the form, 
{{{f(x)=ax^2+bx+c}}}
The axis of symmetry occurs at
{{{x=-b/(2a)}}}
If a is positive, then the mininum value occurs there.
If a is negative, then the maximum value occurs there. 
Comparing your equation to the standard form, 
a=-1
b=-3
The axis of symmetry is
{{{x=-b/(2a)}}}
{{{x=-(-3)/(2*(-1))}}}
{{{x=-3/2}}}
Since a is negative, the value will be a maximum.
The maximum value is,
{{{g(x)=-x^2-3x}}}
{{{g(-3/2)=-(-3/2)^2-3(-3/2)}}}
{{{g(-3/2)=-(9/4)+(9/2))}}}
{{{g(-3/2)=(9/4)}}}
{{{ graph( 300, 300, -5, 1, -10, 10, -x^2-3x) }}}