Question 1085280
use vertex form of equation:

{{{y= a(x-h)^2+k}}} where {{{h}}} and {{{k}}} are {{{x}}} and {{{y}}} coordinates of the vertex, 

if given vertex V ({{{-3}}}, {{{6.5}}}) we have

{{{y= a(x-(-3))^2+6.5}}}

{{{y=a(x+3)^2+6.5}}}

and if passes through P ({{{2}}},{{{6}}}), use it to find leading coefficient {{{a}}}

{{{6=a(2+3)^2+6.5}}}

{{{6=a(5)^2+6.5}}}

{{{6-6.5=25a}}}

{{{-0.5=25a}}}

{{{-0.5/25=a}}}

{{{-0.02=a}}}

so, your equation is: {{{y= -0.02(x+3)^2+6.5}}}


{{{drawing( 600, 600, -30, 30, -30, 30,
circle(2,6,.29), circle(-3,6.5,.29),
locate(2.3,7,p(2,6)),locate(-4,5.5,V(-3,6.5)),
 graph( 600, 600, -30, 30, -30, 30, -0.02(x+3)^2+6.5)) }}}