Question 75527
Using this general equation:

{{{y=a(x-h)^2+k}}} where a is the compression/stretch factor and (h,k) is the vertex. So the equation comes to:

{{{y=a(x-(-4))^2+2}}}
{{{y=a(x+4)^2+2}}}
{{{y=a(x^2+8x+16)+2}}} foil the squared parenthesis
{{{y=ax^2+8ax+16a+2}}} distribute the a
Now plug in the point (3,9)
{{{9=a(3)^2+8(3)a+16a+2}}}
{{{9=9a+24a+16a+2}}}
{{{9=49a+2}}}
{{{7=49a}}}Subtract 2 from both sides
{{{a=1/7}}} Divide both sides by 49

So the equation is 
{{{y=(1/7)(x+4)^2+2}}}

Check:
Plug in (3,9) to see if it works
{{{9=(1/7)(3+4)^2+2}}}
{{{9=(1/7)(7)^2+2}}}
{{{9=(1/7)49+2}}}
{{{9=7+2}}}
{{{9=9}}} works