Question 849018
<pre><font face = "Tohoma" size = 3 color = "indigo"><b> 
Hi,
 y= -3x^2+12x-8
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{x = (-12 +- sqrt( 48))/-6) }}}
{{{x = (-12 +- sqrt( 16*3))/-6) }}}
 {{{x = 2 +-  (-2/3 )sqrt(3)}}}
  midpoint ={{{((2 - (2/3)sqrt(3)) + (2+(2/3)sqrt(3)))/2 }}} = 2  0r simply {{{x = -b/2a)))
V(2,4) (Substituting x = 2 {{{-12+24-8 = 4}}}
Parabola Opening downward:  {{{ y= green(-3)x^2+12x-8}}} 
{{{1/(4a) = -1/12}}}, 4 + (-1/12) = 47/12 Focus(2,47/12)
directrix is y = 4+1/12 = 49/12
{{{drawing(300,300,   -6, 6, -5, 5, grid(1), 
circle(2, 4,0.2),
circle(2, 47/12,0.2),
graph( 300, 300, -6, 6, -5, 5,0,49/12, -3x^2+12x-8 ) )}}}