On the x-y coordinate plane there is a parabola, y=x(6-x). Which of the following points is in the region that is enclosed by this parabola and the x-axis?
I. (1, 1) II. (4, 4) III. (6, 6)  Choices.
A) I only B) II only C) III only D) I and II E) I, II, and III
Since co-efficient of x^2 is negative, the parabola will be downward facing. So the parabola and the x axis will enclose some points where the y-values of the parabola are positive.   When x = 1, y = 5 lies on the parabola, so (1, 1) will be enclosed by the parabola and x axis.   When x = 4, y = 8 lies on the parabola, so (4, 4) will be enclosed by the parabola and x axis.   When x = 6, y = 0 lies on the parabola, so (6, 6) will not be enclosed by the parabola and x axis.   The answer is I and II.
<result>D</result>
On the x-y coordinate plane there is a parabola, y=x(6-x). Which of the following points is in the region that is enclosed by this parabola and the x-axis?
I. (1, 1) II. (4, 4) III. (6, 6)