The function is $\"\"$ .

Where $\"\"$ is the height of the ball above the floor,

$\"\"$ is the forward distance of the ball in front of the foul line,

$\"\"$ is the initial velocity with which the ball is shot in feet per second.

(a)

Find initial velocity when $\"\"$ feet.

The function is $\"\"$ .

From the given data $\"\"$ feet.

$\"\"$

Initial velocity $\"\"$ feet per second.

If $\"\"$ feet per second, $\"\"$ feet.

(b)

The function is $\"\"$ .

Substitute the value of $\"\"$ in the above equation.

$\"\"$

Thus, the function is $\"\"$ .

(c)

Find the height of the ball after it has traveled 9 feet in front of the foul line $\"\"$ .

Forward distance of the ball in front of the foul line $\"\"$ feet.

Consider $\"\"$ .

Substitute the value of $\"\"$ in the above equation.

$\"\"$

The height of the ball after it has traveled 9 feet in front of the foul line is $\"\"$ feet.

(d)

Graph of the function is represents path of the basket ball:

Graph the function $\"\"$ .

Make the table of values to find ordered pairs that satisfy the function.

Choose values for $\"\"$ and find the corresponding values for $\"\"$ .

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

Graph :

1. Draw a coordinate plane.

2. Plot the coordinate points.

3. Then sketch the graph, connecting the points with a smooth curve.

$\"\"$ .

(a) If $\"\"$ feet per second, $\"\"$ feet.

(b) The function is $\"\"$ .

(d)

Graph of $\"\"$ is :

$\"\"$ .