What is the equation of the parabola that has a vertex at (-2, -4) and passes through point (-3,-5) ?

1 Answer
Alan P.
Dec 7, 2015

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

Explanation:

The general vertex form of a parabola with vertex at (a,b) is
color(white)("XXX")y=m(x-a)^2+bcolor(white)("XXX") for some constant m

Therefore a parabola with vertex at (-2,-4) is of the form:
color(white)("XXX")y=m(x+2)^2-4color(white)("XXX") for some constant m

If (x,y)=(-3,-5) is a point on this parabola
color(white)("XXX")-5 = m(-3+2)^2-4

color(white)("XXX")-5 = m - 4

color(white)("XXX")m=-1

and the equation is y=1(x+2)^2-4
graph{-(x+2)^2-4 [-6.57, 3.295, -7.36, -2.432]}

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