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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