Question 316554
The vertex is midway between the 2 roots
When the equation is in the form
{{{ax^2 + bx + c = 0}}}
The formula to find roots is
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
Midway between the 2 roots is {{{x= (-b)/(2a)}}}
{{{3x^2 - 6x - 18 = 0}}}
The x coordinate of the vertex is at {{{(-(-6))/(2*3) = 1}}}
{{{y = 3*1^2 - 6*1 - 18}}}
{{{y = 3 - 6 - 18}}}
{{{y = -21}}}
The vertex is at (1,-21)
Here's the plot
{{{ graph( 500, 500, -10, 10, -25, 10, 3x^2 - 6x - 18) }}}