Question

Find the vertical translation of y=|x| that "supports" the parabola y = x^2. Hint: You should find 'c' so that y = |x|+c just touches y = x^2. You may as well consider only the right-hand side of the picture first. (Why?)

Answer 1

slope of parabola=2x
slope of lines=1
so x where touching is x=1/2
so y=abs x + b is one equation
y=x^2 is the other.

y=abs x+b
1/4=abs(1/2)+b
b=-1/4