Parabola and triangle area

Arthur Lee
A straight line cuts a parabola at two points, A and B. C is a movable point on the parabola between A and B. What should be the position of C to make the biggest triangle? You may zoom in to adjust point C in a smaller range during your exploration.

Question 1

Share your findings here. What do you notice about the position of C when the area of the triangle is maximum?

Question 2

You may change the functions for the line and parabola on the left to further explore how the maximum area is found in other cases. How do you change the functions? Will you get the maximum area again in the way you describe C in question 1?

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