Question

Let p(x,y) be a point on the graph of y=x^3-2. Express the distance d from P to the origin O as a function of x.

Answer 1

\[d=\sqrt{\left( x-0 \right)^2+\left( y-0 \right)^2}=\sqrt{x^2+y^2}\]
\[=\sqrt{x^2+\left( x^3-2 \right)^2}\]