How to find the equation of a Parabola with vertex (0,-9) and passing through (6,-8)?

1 Answer
Alan P.
Jul 23, 2015

#y = x^2/36 -9#

Explanation:

The general vertex form for a parabola is
#color(white)("XXXX")##y = m(x-a)^2+b#
#color(white)("XXXX")##color(white)("XXXX")#where the vertex is at #(a,b)#

Given that the vertex of the desired parabola is at #(0,-9)#
this becomes:
#color(white)("XXXX")##y = m(x-0)^2-9#

and since #(x,y) = (6,-8)# is a solution point on this parabola:
#color(white)("XXXX")##-8 = m(6-0)^2-9#

#color(white)("XXXX")##1 = 36m#

#color(white)("XXXX")##m = 1/36#

Therefore
#color(white)("XXXX")##y = 1/36(x-0)^2-9#
or
#color(white)("XXXX")##y = x^2/36 -9#

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