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.

Pls help, also do i find how long and how high the ball reached or how long it took the basketball to reach the ground. Please answer them as well. Thank you so much.

Answer 1

y = 9 at x = 2 seconds

y = 0 at x = 5 seconds

Explanation:

y=-x^2+4x+5

First find the zeros

0 =-x^2+4x+5

0 = -(x^2 -4x -5)

What 2 numbers multiply to -5 and add to -4

-5*1 = -5

-5+1 = -4

0 = -(x-5)(x+1)

x-5 =0 x+1 =0

x=5 x =-1

The vertex is 1/2 way between the two zeros

(5+-1) /2 = 4/2 =2

The vertex is at x=2

The maximum value of y is when x=2

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

y = -4+8+5

y = 9

The ball will hit the ground at x = 5 seconds