From the graph plotted, the time when the ball is kicked is 0 second.
The time when the ball hits the ground is 2 seconds.
How to determine the time when the ball is kicked?
The time when the ball is kicked calculated as follows;
The given function
y = -16x² + 32x
when the ball is kicked, the height of the ball is zero, y = 0, and time = 0
The time when the ball reaches maximum height is calculated as follows;
at maximum height, the final velocity of the ball is zero, v = 0
y = -16x² + 32x
v = dy/dx
v = -32x + 32
v = 0
0 = -32x + 32
32x = 32
x = 32/32
x = 1 second
The time when the ball hits the ground; y = 0
0 = -16x² + 32x
32x = 16x²
32 = 16x
x = 32 / 16
x = 2 seconds
From the graph plotted, we can see that;
the time when the ball is kicked, time = 1 second and height = 0
the time when the curve is on ground level (0), time = 2 seconds.