What is the equation of the parabola that has a vertex at # (-2, -4) # and passes through point # (-3,-15) #?

1 Answer
Alan P.
Feb 17, 2016

#y=-11(x+2)^2-4#

Explanation:

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

Since the required parabola has a vertex at #(-2,-4)# this becomes:
#color(white)("XXX")y=m(x+2)^2-4#

and since #(x,y)=(-3,-15)# is a solution to this equation:
#color(white)("XXX")-15=m(-3+2)^2-4#

#color(white)("XXX")-11 = m

So the equation of the parabola can be written as
#color(white)("XXX")y=(-11)(x+2)^2-4#

graph{-11(x+2)^2-4 [-12.24, 13.06, -16.24, -3.59]}

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