The curve C has equation y = x^3 - 2x^2 - x + 9, x > 0. The point P has coordinates (2, 7). Show that P lies on C.

Every point on the curve C satisfies the equation. In order to show P lies on C, we need to test if either x- or y-coordinates satisfy the equation. It is easier to subsitute x=2 into the equation.

By doing so, this gives

y = (2)³ - 2 x (2)² - (2) + 9 

y = 7

As P's y-coordinate is also 7, therefore, P (2, 7) lies on the curve C.