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

Answer:

After two seconds, the ball reached 9 units up.

Step-by-step 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 $h=-\frac{b}{2a}$ and $k=f(h)$.

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

$h=-\frac{4}{2(-1)}=2$

$k=f(2)=-(2)^{2} +4(2)+5=-4+8+5=9$

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.