Question 666191
{{{f(x) = a(x - h)^2 + k }}}....vertex form

vertex({{{2}}},{{{3}}}) and point ({{{0}}},{{{23}}})

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

{{{f(x) = a(x^2 - 4x+4) + 3}}}

use point ({{{0}}},{{{23}}}) to find {{{a}}}

{{{f(x) = a(x^2 - 4x+4)+3 }}}

{{{23-3 = a(0^2 - 4*0+4) }}}

{{{20= 4a}}}

{{{20/4= a}}}

{{{ a=5}}}

plug it in {{{f(x) = a(x^2 - 4x+4) + 3}}}

{{{f(x) = 5(x^2 - 4x+4) + 3}}}

{{{f(x) = 5x^2 - 20x+20+ 3}}}

{{{f(x) = 5x^2 - 20x+23}}}........the standard form


{{{drawing(600,600,-5,5,-5,25,grid(0),circle(2,3,0.1),locate(2,3-.2,"V(2,3)"),
locate(0,23-.2,"P(0,23)"),circle(0,23,0.1),graph(600,600,-5,5,-5,25,5x^2 - 20x+23))}}}