Question

Harshdeep was playing basketball with his friends with seconds left before the game ended he attempted a 3 point shot the following equation models the path of the basketball y=-x^2+4x+5 where x is the elapsed time in seconds

Answer 1

After two seconds, the ball reached 9 units up.

Explanation:

The given function is

`y=-x^(2) +4x+5`

The given function models the path of the ball.

The maxium height the ball reached is given by the vertex of this function, which has coordinates
`V(h,k)`, where
`h=-(b)/(2a)` and
`k=f(h)`.

From the equation, we know that
`a=-1`,
`b=4` and
`c=5`. Replacing these values, we have

`h=-(4)/(2(-1))=2`

`k=f(2)=-(2)^(2) +4(2)+5=-4+8+5=9`

Where
`k` determines the height and
`h` the time when the maximum height was reached by the ball.

The maximum height is 9 units.

Therefore, after two seconds, the ball reached 9 units up.