What is the equation of the parabola that has a vertex at # (33, 11) # and passes through point # (23,-6) #?

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Answer 1 · 2017-07-15T11:41:21

The equation of parabola is #y= -0.17(x-33)^2+11#.

The standard equation of parabola in vertex form is
#y= a(x-h)^2+k ; (h,k)# being vertex. # h=33, k=11#

The equation of parabola is #y= a(x-33)^2+11#.

The parabola passes through #(23,-6)# . The point will satisfy the equation of parabola.

#-6 = a(23-33)^2+11 or -6 = 100a +11# or

#100a = -17 or a = -0.17#

So the equation of parabola is #y= -0.17(x-33)^2+11#.

graph{-0.17(x-33)^2+11 [-80.2, 80.2, -40.1, 40.1]} [Ans]