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

Question

4118 views around the world

You can reuse this answer
Creative Commons License

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.
enter image source here
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#