Question 731342
given:

vertex = ({{{-2}}},{{{6}}}) and {{{y-intercept = -2}}}

Step 1:

The standard equation of parabola when the vertex is along {{{y}}} intercept is given by:

{{{ (x-h)^2=4p(y-k)}}} where vertex:({{{h}}},{{{k}}}) = ({{{-2}}},{{{6}}})

and {{{p= y-intercept = -2}}}

Step 2: 

Putting values of {{{h}}}, {{{k}}} and {{{p}}} in the standard equation and simplifying you get:


{{{(x-(-2))^2 =4(-2)(y - 6)}}}

{{{(x+2)^2 =-8(y - 6)}}}
	
{{{x^2 + 4x + 4 = -8y + 48}}}

{{{8y =-x^2 -4x +44 }}} 

{{{y =(-1/8)x^2 -(1/2)x +11/2 }}}is the required equation of parabola.This is the answer.


{{{ graph( 500, 500, -10, 10, -5, 10, (-1/8)x^2 -(1/2)x +11/2) }}}