Question

Anastasia hits her golf ball off the tee. The height of the golf ball is modeled by the function f(x) =-5x^2+25x+1, where x is the number of seconds after the golf ball is hit. How long is the golf ball in the air? ​

Answer 1

9514 1404 393

Answer:

5.04 seconds

Explanation:

Assuming the ball is in the air until f(x) = 0, we want to find x such that ...

0 = -5x² +25x +1

0 = x² -5x -1/5 . . . . . divide by -5

1/5 = x² -5x . . . . . . . add 1/5

1/5 +25/4 = (x² -5x +25/4) . . . . complete the square

129/20 = (x -5/2)² . . . . . . . . . . write as a square

x = 5/2 +√(129/20) ≈ 5.039685 . . . . square root, add 5/2

The ball stays in the air about 5.04 seconds.