How do I sketch a curve with equation y = x(x-2)^2 ?

Answer 1

Expand first the equation. Find the intercepts. Find the domain and range of the function.

The intercepts will serve as the turning points. Since the leading coefficient (of x^3) is positive, the graph of f is up on the right and down on the left and hence the range of f is the set of all real numbers.

Or to make it simple, assign values of x and y and place it in a table. Plot the points in the graph and connect the dots.

Answer 2

the turning points are in between the x-intercepts.