Given the equation (x+4)^2 = -12y + 24 determine: a)  The Vertex b)  If the parabola opens up, down, left, right c)  The Focus

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Equation of the parabola is

`(x+4)^2=-12(y-2)`

Parabola is defined if `y<=2`

1. Vertex of the parabola

x+4=0

x=-4 and

y-2=0

y=2

Thus vertex is (-4,2)

2 Since parabola is defined only if `y<=2`

This shows parabola open down.

3. Focus of the parabola

let

X=x+4  and  Y=y-2

`X^2=4(-3)Y`

`Thus ` focus of the transformed parabola is (0,-3)

Thus focus of orinal parabola is  (-4,2-3)=(-4,-1)

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