How do you write the equation of the parabola in vertex form given points (3,1) the vertex(5,9)?

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Answer 1 · 2017-07-23T05:15:10

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

Given -

#(3,1)# [point on the parabola]
Vertex #(5,9)#

Formula for the parabola in vertex form

#y=a(x-h)^2+k#

Here #(h,k)# coordinates of the vertex.
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Let us substitute #(5,9)# in the formula.

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

To find the value of #a#, substitute #(3,1)#

#1=a(3-5)^2+9#
#1=a4+9#

Solve for #a#

#4a+9=1#
#4a=1-9=-8#
#a=-8/4#

#a=-2#

The equation is -

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