Question #7c39a

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Answer 1 · 2018-02-11T03:10:42

#(1,1.5)#

Let's rewrite this into form #4p(y-k)=(x-h)^2#

#y=1/2(x-1)^2+1#

=>#y-1=1/2(x-1)^2#

=>#2(y-1)=(x-1)^2#

We now compare this to #4p(y-k)=(x-h)^2#

#2(y-1)=(x-1)^2#
#4p(y-k)=(x-h)^2#

It seems to us that:
#h=1#
#k=1#
#4p=2#

Let's solve for #p#.

#4p=2#

=>#p=1/2#

Now, since #x-h# is being squared, this parabola opens vertically and therefore we deal with #k# for the focus.

The focus is #(h,k+p)# for any horizontal parabola.

Therefore, the focus is:
#(1,1+1/2)#

=>#(1,1.5)#

That is our answer!