Question 588865
{{{ -3x^2 + 6x + 9 }}}
{{{ a*( x - h )^2 + k }}}
{{{ a*( x^2 - 2*h*x + h^2 ) + k }}}
{{{ a*x^2 - 2*a*h*x + a*h^2 + k }}}
(1) {{{ a = -3 }}}
(2) {{{ -2*a*h = 6 }}}
(3) {{{ a*h^2 + k = 9 }}}
This is 3 equations and 3 unknowns, so
it should be solvable
Plug (1) into (2)
(2) {{{ -2*(-3)*h = 6 }}}
(2) {{{ 6h = 6 }}}
(2) {{{ h = 1 }}}
and
(3) {{{ -3*1^2 + k = 9 }}}
(3) {{{ -3 + k = 9 }}}
(3) {{{ k = 12 }}}
so,
{{{ -3x^2 + 6x + 9  = -3*( x - 1 )^2 + 12 }}}
check answer:
{{{  -3*( x - 1 )^2 + 12 }}}
{{{ -3*( x^2 - 2x + 1 ) + 12 }}}
{{{ -3x^2 + 6x - 3 + 12 }}}
{{{ -3x^2 + 6x + 9 }}}
OK