Question 887945
Begin filling-in standard form equation.  You know from those three points, {{{a>0}}}.
<i> intercepts of x = -2, x = 3, and y = -4</i> means x for the vertex is {{{(-2+3)/2=1/2}}}.

{{{y=a(x-h)^2+k}}}
What happens if solve for a?
{{{a(x-h)^2=y-k}}}
{{{a=(y-k)/(x-h)^2}}}
-
The two roots give{{{ a=(-k)/(-2-h)^2}}} and {{{a=(-k)/(3-h)^2}}}.  Might be helpful now or maybe later.


We can also do this based on the two roots.
{{{y=a(x+2)(x-3)}}}
NOW try solving for a from this equation.
{{{a=y/((x+2)(x-3))}}}
Substitute for the y-intercept:
{{{a=-4/((0+2)(0-3))}}}
{{{a=-4/(-6)}}}
{{{highlight_green(a=2/3)}}}
Our equation can be stated, not standard form but as a factored form {{{highlight(y=(2/3)(x+2)(x-3))}}}.


We already saw what is x of the vertex and now we can find the y coordinate.
{{{y=(2/3)(1/2+2)(1/2-3)}}}
{{{(2/3)(5/2)(-5/2)=-(2*5*5)/(3*2*2)}}}
{{{highlight_green(y=-25/6)}}}


Going back to finish standard form, {{{highlight(highlight(y=(2/3)(x-1/2)^2-25/6))}}}.


That should be sufficient for you to answer the other questions also.