A parabola has a maxima at #(-4,7)# and passes through #(1,1)#. Which is the other point with same ordinate that it passes through?

1 Answer
Nov 2, 2016

Answer:

Parabola also passes through #(-9,1)#

Explanation:

We can use here vertex form of equation for parabola. As it has a maximum at #(-4,7)#, it will be of the form

#y=-a(x+4)^2+7#

Note that at #(-4,7)#, #y# has a maximum value of #-7# as #a(x+4)^2=0# and at other places as it is negative, value of #y# is far less.

Now as #y=-a(x+4)^2+7# passes through #(1,1)#, we have

#1=-a(1+4)^2+7# or #1=-25a+7# i.e. #25a=6# and

#a=6/25# and equation of parabola is #y=-6/25(x+4)^2+7#

Note that this form of equation is symmetric w.r.t. #x+4=0# and hence The point symmetric to #(1,1)# will have abscissa given by #(x+1)/2=-4# i.e. #x=-9# and then

#y=-6/25(-9+4)^2+=-6/25xx25+7=1# i.e.

Parabola also passes through #(-9,1)#
graph{-6/25(x+4)^2+7 [-14.17, 5.83, -2.2, 7.8]}