What is the minimum vertical distance between the parabolas y=x^2+1 and PS

tabita57i

tabita57i

Answered question

2021-09-22

What is the minimum vertical distance between the parabolas y=x2+1 and y=xx2

Answer & Explanation

Sally Cresswell

Sally Cresswell

Skilled2021-09-23Added 91 answers

y1=x1+1, y2=xx2
The vertical at any point x is obtained form
D=y1y2=x2+1(xx2)
=x2+1x+x2
=2x2x+1
If you subtract the other way the distance you get is negative because of where the graphs are situated, but the problem would work out similarly.
Find where D=0
D(x)=0=4x1
x=14
D(x)=2x2x+1 is an upward opening parabola so x=14 is the minimum.
Plug in to get the minimum distance
D(14)=2(14)214+1
=1814+1
=12+88
=78
Result: 78

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?