# Thread: Parabola Question - Urgent

1. ## Parabola Question - Urgent

A person is building a dome shaped display cabinet with its edge modelled by the equations $a(x) = -0.5x^2 + 90$. Assume the base of the cabinet is the x-axis.

If the shelves are to be built at 20 cm intervals (from the base). Find the coordinates of each end of the four shelves.

2. Originally Posted by mibamars
A person is building a dome shaped display cabinet with its edge modelled by the equations $a(x) = -0.5x^2 + 90$. Assume the base of the cabinet is the x-axis.

If the shelves are to be built at 20 cm intervals (from the base). Find the coordinates of each end of the four shelves.
I'll do the first one.
The first shelf is 20 cm above the base, so $a(x) = 20$ where x is the coordinate of either end. (If you look at the graph of a(x) you'll see it's centered on the y-axis.) Thus we need to solve:
$20 = -0.5x^2 + 90$

$0.5x^2 = 70$

$x^2 = 140$

$x = \pm \sqrt{140} = \pm 2 \sqrt{35}$

So the ends of the first shelf are at
$(-2 \sqrt{35}, 20) \text{ and } (2, 2 \sqrt{35})$

Can you do the other 3 shelves?

-Dan