What is the equation of the parabola that has a vertex at # (2, -5) # and passes through point # (3,-105) #?

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Answer 1 · 2016-02-22T17:07:35

#y = -100 (x-2)^2 - 5#

Note: The standard form of a parabola is #y = a(x-h)^2 + k# , in which the #(h, k)# is the vertex.

This problem given the vertext #(2, -5)# , which mean #h = 2, k = -5#

Passes through the point #(3, -105)# , which mean that #x = 3, y = -10#

We can find #a# by substitute all the information above into the standard form like this

#y = a( x-h)^2 + k#
#y = a(x-color(red)(2))^2 color(red)(-5)#

#color(blue)(-105) = a(color(blue)(3-color(red)(2)))^2color(red)(-5)#

#-105 = a(1)^2 - 5#

#-105 = a -5#

#-105 + 5 = a#

#a = -100#

The standard equation for the parabola with the given condition is

#y = -100 (x-2)^2 - 5#