Question 38158
Hey ... we did this one on the phone today. :)  Glad you made it to the site :)

{{{ y = -4x^2 +16x - 12 }}}
For the intercepts, assume y = 0
{{{ 0 = -4x^2 +16x - 12 }}}
Divide by -4 throughout
{{{ 0 = x^2 + 4x - 3 }}}
factor
{{{ 0 = (x-3)(x-1) }}}
set both parts equal to 0
{{{ 0 - x-3 }}} and {{{ 0 = x - 1 }}}
x = {1, 3}


Now for the line os symmetry ... {{{ x = -b/2a }}}
use the +16 from the Original equation
{{{ x = -16/2(-4) }}}
{{{ x = -16/-8 }}}
{{{ x = 2 }}}
Well, yes, 2 is 1/2 way between 1 and 3 so this makes sense.
Plug this x value into the original equation.

{{{ y = -4x^2 +16x - 12 }}}
{{{ y = -4(2)^2 +16(2) - 12 }}}
{{{ y = -4(4) +16(2) - 12 }}}
{{{ y = -16 +16(2) - 12 }}}
{{{ y = -16 +32 - 12 }}}
{{{ y = 16 - 12 }}}
{{{ y = 4 }}}
so now your Vertex is (2,4)
your three point to graph are:
(1,0)  (3,0)  (2,4)
the vertex is a maximum and the Parabala opens down because the leading coefficient is negative.