+296 A triangle is formed with one vertex at the vertex of the parabola y=x^2-1 and the other two vertices at the intersections of the line y=r and the parabola. If the area of the triangle is between 8 and 64 inclusive, find all possible values of r. Express your answer in interval notation.
+129899 By the graph here : https://www.desmos.com/calculator/zascepyruy
Note that :
The height of the triangle = x^2
And the base of the triangle = 2x
So we have that
(1/2) x^2 * ( 2x ) = 8
x^3 = 8
x = 2
So the minimum possible height = 2^2 = 4
So y = 3
And
(1/2) x^2 * (2x) = 64
x^3 = 64
x = 4
So....the max possible height = 4^2 = 16
So y = 15
So
3 ≤ r ≤ 15
