A parabola has a vertex at (3, 5) and contains the point (0,0). If this function is a parabola, how do you find its equation?

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Answer 1 · 2016-12-05T17:30:07

#y=-5/9(x-3)^2+5#

The general formula of a parabola with vertex in #(x_v,y_v)# is:

#y=a(x−x_v)^2+y_v#

Here #(x_v,y_v)# is #(3,5)#, so:

#y=a(x-3)^2+5#

If the parabola contains the point #(0,0)# this equation must be satisfied when substituting #x=0# and #y=0#, and this allows us to determine #a#:

#0=9a+5#

#a=-5/9#

The equation of the parabola is then:

#y=-5/9(x-3)^2+5#

graph{-5/9*(x-3)^2+5 [-9.46, 10.54, -3.6, 6.4]}