# Key Components of Functions and Graph Verbally

The height h(t) in feet above the ground of a golf ball depends on the time, t (in seconds) it has been in the air. Ed hits a shot off the tee that has a height modeled by the velocity function h(t) = 0.5at^2 + vt + s where a is -32 ft/sec^2, v is the initial velocity, and s is the initial height.

1. Write a function that models the situation.

2. Sketch a graph of the function and describe the graph verbally.

3. Identify the key components of the graph (minimum or maximum, vertex, roots) and give a brief description of what each represents.

4. What is the height of the ball at 1.5 seconds? Is there another time at which the ball is at the same height?

5. At what time (s) will the ball be 48 feet above the ground?

6. How long after the ball is in the air does it reach its maximum height?

7. After how many seconds will the ball hit the ground?

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#### Solution Preview

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MODELLING:

The general modelling equation for the height at time is given by (1)

(1)

Where acceleration due to gravity, (in the vertical direction) and (tee height above the ground)

The speed at which the ball is hit in a direction with the ground we assume is and thus by considering vectors we have a vertical component of velocity

Thus on substitution into the general model we get (2)

(2)

This model (2) describes the vertical height of the golf ball at any

subsequent time when driven at a velocity in any particular direction

with respect to the horizontal ground

Now to try and describe a typical situation we need to assume some initial conditions. Let us consider ...

#### Solution Summary

The expert examines the key components of functions and graphs verbally.