Maths question?

Question

X is a point on the curve y=x^2-2x+5. Point Y lies directly below X and is on the curve y=4x-x^2.

a) show that the distance d between x and y is given by
d=2x^2 - 6x + 5.

Answer 1

X is a point on the curve y=x^2-2x+5. Point Y lies directly below X and is on the curve y=4x-x^2.

a) show that the distance d between x and y is given by

d=2x^2 - 6x + 5.



Since Y lies directly below X both X and Y have same value for x co-ordinate

Let X be (x, x²-2x+5) and Y be (x,4x-x²)

Distance between 'd' X and Y is given by the difference of y coordinates of X and Y

i.e. d=(x²-2x+5) - (4x-x²)=2x²-6x+5

Answer 2

http://www.wolframalpha.com/input/?i=graph+x%5E2-2x%2B5+and+4x-x%5E2

distance between x and y = x^2-2x+5-(4x-x^2)

= x^2-2x+5-4x+x^2

= 2x^2-6x+5

Answer 3

ur nan

Answer 4

Here is the situation

https://www.wolframalpha.com/input/?i=y+%3D+x%5E2+-+2x+%2B+5,+y+%3D+4x+-+x%5E2,+(x+from+-+1+to+4)



General expression for vertical distance apart for any x value

x^2 -2x + 5 – (4x - x^2) = 2x^2 – 6x + 5