Question 131739
The vertex is at {{{x = (-b)/(2a)}}}
where the equation is in the form
{{{y = ax^2 + bx + c}}}
Your equation is:
{{{y = -2x^2 - 3x + 8}}}
{{{a = -2}}}
{{{b = -3}}}
{{{c = 8}}}
{{{(-b)/(2a) = (-(-3))/(2*(-2))}}}
{{{(-b)/(2a) = -(3/4)}}}
{{{x = -(3/4)}}}
Now I have to find {{{y}}}
{{{y = -2*(-(3/4))^2 - 3*(-(3/4)) + 8}}}
{{{y = -(18/16) + 9/4 + 8}}}
{{{y = -(9/8) + 18/8 + 64/8}}}
{{{y = 73/8}}}
The vertex is at (-3/4 , 73/8)
I'll plot this to check
 {{{ graph( 600, 600, -4, 4, -4, 12, -2x^2 - 3x + 8) }}}