What is the equation of the parabola that has a vertex at # (-2, 4) # and passes through point # (2,19) #?

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Answer 1 · 2016-01-14T00:16:46

The equation of the parabola can be written:

#y = 15/16(x+2)^2+4#

In general a parabola with vertical axis and vertex #(h, k)# can be written in the form:

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

So, assuming the axis of the parabola is vertical, its equation can be written in the form:

#y = a(x+2)^2+4#

for some constant #a#.

Then substituting #x=2# and #y=19# into the equation we get:

#19 = a(2+2)^2+4 = 16a+4#

Hence #a = (19-4)/16 = 15/16#

So:

#y = 15/16(x+2)^2+4#