Question

Jake tosses a coin up in the air and lets it fall on the ground. The equation that

models the height (in feet) and time in seconds) of the parabola is
- -16t2 + 24 + 6. When does the coin reach its greatest height?

Answer 1

The coin will reach the maximum height of 15 feet in
`(3)/(4)` second

Explanation:

The equation that models the height (in feet) and time in seconds) of the parabola is

`h(t)=-16t^2 + 24t + 6`

The coin will reach its greatest height at the parabola's vertex. Find the coordinates of the vertex.

From the function expression:

`a=-16\\ \\b=24\\ \\c=6`

Now,

`t_v=(-b)/(2a)\\ \\=-(24)/(2\cdot (-16))\\ \\=(24)/(32)\\ \\=(3)/(4)\ second`

Then

`h_v=h(t_v)\\ \\=-16\cdot \left((3)/(4)\right)^2+24\cdot (3)/(4)+6\\ \\=-16\cdot (9)/(16)+18+6\\ \\=-9+24\\ \\=15\ feet`