Question 1176762

given:

Vertex ({{{2}}},{{{3}}}); passing through ({{{1}}},{{{6}}})


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


if vertex ({{{2}}},{{{3}}}) => {{{h=2}}} and {{{k=3}}}


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


if the parabola passing through ({{{1}}},{{{6}}})

{{{6 =a(1-2)^2+3}}}.........solve for {{{a}}}

{{{6 =a(-1)^2+3}}}
{{{6-3 =a*1}}}
{{{a=3}}}

and equation is:

{{{f(x) =3(x-2)^2+3}}}


{{{drawing( 600, 600, -10, 10, -10, 10,
circle(2,3,.12),locate(2,3,V(2,3)),
circle(1,6,.12),locate(1,6,p(1,6)),

 graph( 600, 600, -10, 10, -10, 10, 3(x-2)^2+3)) }}}