What is the equation of the parabola that has a vertex at # (-8, 5) # and passes through point # (2,27) #?

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Answer 1 · 2016-03-20T07:04:08

#(x--8)^2=+(50/11)(y-5)" "#Vertex Form

From the given: Vertex (-8, 5) and passing thru (2, 27), the parabola opens upward. The reason is that the vertex is lower than the given point.

By the vertex form , we can solve for the value of #p#

#(x-h)^2=+4p(y-k)#

#(2--8)^2=+4p(27-5)#

#10^2=4p(22)#

#100=4(22)p#

#25=22p#

#p=25/22#

Go back to the vertex form

#(x--8)^2=+4(25/22)(y-5)#

#(x--8)^2=+2(25/11)(y-5)#

#(x--8)^2=+(50/11)(y-5)" "#Vertex Form

graph{(x--8)^2=(50/11)(y-5)[-50,50,-25,25]}

God bless....I hope the explanation is useful.