Question

Nancy throws a ball toward a basket 3.2 m off the ground. The rule associated with the ball's trajectory is `y = -.4(x-6)^2 + 3.6`. Nancy throws the ball at a distance of 3 m from the basket. From what height did Nancy throw the ball?

Answer 1

Assuming we don't have to travel into the basket on the downward arc, Nancy threw the ball from a height of 2m

Explanation:

First, we need to know what the x value is in the trajectory equation that satisfies the basket height (`y=3.2`):

`3.2=3.6-0.4(x-6)^2`
`-0.4=-0.4(x-6)^2`
`x-6=1 rArr x=7`

we know that Nancy threw the ball 3m from the basket, meaning she was at a distance of `7-3=4m`. Plugging that into the trajectory equation gives us our launch height:

`y=3.6-0.4(4-6)^2 rArr y=3.6-0.4(-2)^2`
`y=3.6-0.4*4 rArr y=3.6-1.6`
`color(red)(y=2m)`