Question 1194461


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

if a vertex at the​ origin, means {{{h=0}}} and {{{k=0}}}

{{{y = a(x - 0)^2 + 0}}}

{{{y = ax^2 }}}

if passing through ({{{sqrt(3)}}},{{{12}}})​=>{{{x=sqrt(3) }}}and {{{y=12}}}

use it to calculate {{{a}}}

{{{12= a(sqrt(3))^2 }}}

{{{12= a(3)}}}

{{{a=12/3}}}

{{{a=4}}}

so, your equation is {{{y = 4x^2 }}}



{{{ drawing( 600, 600, -15, 15, -15, 15,
circle(sqrt(3), 12,.12), locate(sqrt(3), 12,p(sqrt(3), 12)),
graph( 600, 600, -15, 15, -15, 15, 4x^2)) }}}