Question

Pre-calculus 12 question!

Answer 1

well, the height of the rectangle is given by the equation y = 9 - x^2
and the width is 2x

Answer 2

Ok

Answer 3

so area = ?

Answer 4

I know how to get the area, but how do you know the height?

Answer 5

@Vocaloid

Answer 6

well, think of it this way:

on the x-y coordinate plane, the x value tells you how far to the right or left to go, and the y-value tells you how far up or down to go, correct?

since we want the height of the rectangle, it naturally follows that we want the y value

Answer 7

yes correct

Answer 8

so, we're given the equation y = 9 - x^2, so that's our height

Answer 9

but the height of the rectangle is far smaller than the original prabola

Answer 10

nope, not necessarily, remember that x is not a fixed value

if we make x something super small, like 0.00001, then the height of the rectangle is almost the height of the parabola

the point is that x changes

Answer 11

ok I got this, and about the width, it looks like 4x to me. How is it 2x?

Answer 12

well, think of it this way.

let's try splitting the rectangle in half down the y-axis, like this: