Question

Let P=(x,y) be a point on the graph of y=x^2-9. Express the distance d from P to the origin as a function of x.

Answer 1

We have :
\[OP=\sqrt{(x_p-x_o)^2+(y_p-y_o)^2}=\sqrt{x^2+\left(x^2-9\right)^2}=\sqrt{x^4-17x^2+81}\]