Answer:
Time taken to reach the maximum height = 1.43 seconds
Maximum height of the ball = 18.29 feet
Time taken to return to the ground = 2.86 seconds
Explanations:
The function representing the height of the softball at time x seconds is given as:
[tex]y=-7x^2\text{ + 20x + 4}[/tex]
The graph of the quadratic function is plotted below:
At maximum height, dy/dx = 0
For y = -7x² + 20x + 4
dy/dx = -14x + 20
Since dy/dx = 0 at maximum height
-14x + 20 = 0
14x = 20
x = 20 / 14
x = 1.43 seconds
Time taken by the soft ball to reach its maximum height = 1.43 seconds
To find the maximum height of the soft ball, substitute x = 1.43 into
y = -7x² + 20x + 4
y = -7 (1.43)² + 20(1.43) + 4
y = -14.31 + 28.6 + 4
y = 18.29 feet
The time it takes the soft ball to return to the ground
This will be double of what it takes to reach the maximum height = 2 x 1.43 = 2.86
The time it takes the ball to return to the ground = 2.86 seconds
