what is the maximum vertical distance between the line y = x +2 and the parabola y = x^2 for -1 greater than equal x smaller than or equal 2 ?

Solution:

For -1<=x<=2

The vertical distance = |x^2-(x+2)|= |(x-0.5)^2 -2.25|

so when x=0.5, the vertical distance is max, it's 2.25.