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.

EpicWater Dec 31, 2019

#1**+1 **

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

CPhill Jan 1, 2020