Question

A ball is thrown off the roof of the school. Its path can be described by the equation: h(t) = -2t^2 + 8t + 10, where h is height in meters after t seconds.

a) How tall is the building?

Answer 1

10 meters

Explanation:

The given function
`h(t)=-2t^2+8t+10` represents the height,
`h`, in meters,
`t` seconds after the ball is thrown.

Since the ball is thrown off the roof, then ball's height will be equal to the roof's height before being thrown (0 seconds). Therefore, substitute
`t=0` into the given function
`h(t)=-2t^2+8t+10`:

`h(0)=-2(0^2)+8(0)+10,\\h(0)=0+0+10,\\h(0)=\boxed{10\text{ meters}}`

Therefore, the building is 10 meters tall.