Thread: Dividing a parabola into 3 equivilant areas?

1. Dividing a parabola into 3 equivilant areas?

If I have a parabola with the equation -(x-4)^2+5 how would I go about dividing it into three equal areas using two lines that meet at the same point at the top-center of the parabola and both touch the axis?

Attached is a small illustration of what I am trying to do.

2. typo

Originally Posted by Shivian
If I have a parabola with the equation -(x-4)^2+5 how would I go about dividing it into three equal areas using two lines that meet at the same point at the top-center of the parabola and both touch the axis?

Attached is a small illustration of what I am trying to do.
1. Calculate the area included by the x-axis and the parabola. $\left(\dfrac{20}3 \sqrt{5}\right)$

2. Calculate the area of the isosceles triangle.

3. Since you already know the height of the triangle (h = 5) you can calculate the length of the base.

4. Since the base must be symmetric to x = 4 you can get the start and endpoint of the base. I've got $S(4-\frac49\sqrt{5} , 0)\ and \ E(4+\frac49\sqrt{5} , 0)$