** **

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 the height of the ball after it has traveled 8 feet in front of the foul line().

Initial velocity feet per second.

Forward distance of the ball in front of the foul line feet.

Consider .

Substitute the values of and in the above equation.

The height of the ball after it has traveled 8 feet in front of the foul line is 10.4 feet.

** **

(b)

Find the height of the ball after it has traveled 12 feet in front of the foul line().

Initial velocity feet per second.

Forward distance of the ball in front of the foul line feet.

Consider .

Substitute the values of and in the above equation.

The height of the ball after it has traveled 12 feet in front of the foul line is 9.9 feet.

(c)

The function is .

Rewrite the function as .

Substitute the values of in the above equation.

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.

.

(d)

The ball will not go through the hoop.

Because from the given data :

If a player shoots a foul shot, releasing the ball at a angle from a position 6 feet above the floor, then the path of the ball can be modeled by the function .

Since the center of the hoop is 10 feet above the floor and 15 feet in front of the foul line, the ball will not go through the hoop.

Observe the graph of the function feet.

Find initial velocity when feet.

The function is .

From the given data feet.

Initial velocity feet per second.

If feet per second, feet.

(a) The height of the ball after it has traveled 8 feet in front of the foul line is 10.4 feet.

(b) The height of the ball after it has traveled 12 feet in front of the foul line is 9.9 feet.

(c)

Graph of is :

(d)

The ball will not go through the hoop ; feet.

If feet per second, feet.

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