Question 1010822
Two of the points are obvious zeros or roots.  


You could quickly start with  {{{y=a(x-8)(x+2)}}}.  The point (0,8) can be used now to determine the value for a.  Not yet then in standard form, but realize, you can find the vertex, knowing the symmetry axis is exactly in the middle of  x at 8 and x at -2; or {{{x=3}}}; and you had found a; right?




{{{a=y/((x-8)(x+2))}}}
-
{{{a=8/((-8)(2))}}}
{{{highlight_green(a=-1/2)}}}



Another way to finish, is do the multiplying in {{{y=-(1/2)(x-8)(x+2)}}} and then use Completing the Square to put into standard form, but if you can just use the middle value between the zeros,....,......!