1. The problem statement, all variables and given/known data Triangle OAB is an isosceles triangle with vertex O at the origin and vertices A and B on the parabola y = 9-x^2 Express the area of the triangle as a function of the x-coordinate of A. 2. Relevant equations A = 1/2 bh Distance formula (maybe) Heron's Formula (an alternative) 3. The attempt at a solution The area of a triangle is given by A = 1/2 bh. If point A is (x, 9 - x^2), then b=2x and h = 9-p^2 The final equation will be A = 9x - x^3 (as a function of the x coordinate of A) The equation above works only for a limited number of triangles embedded in the parabola. For instance, if A and B has the same x coordinates, then the equation will work. But i considered two different triangles that can make an isosceles triangle: O = (0,0) A = (2,5) B = (2,5) Area is 10 unites^2 and O = (0,0) A = (2,5) B = (-2.2777902,3.8111609) And the area will be around 4.75 units^2 Both of those are isosceles triangles, that can fit into the parabola of 9-x^2. How would I go about finding an equation that can find the area of all possible isosceles triangles in the parabola?