Do Now: The height, in feet, of a ball thrown into the air is modeled by h(t) = - 16t 2 – 96t , where t is measured in seconds. Graph the height of the ball seconds on the following grid. Use a scale on the x -axis of 3 boxes = 1 second. On the y -axis use 5 boxes = 40 feet.

How far did the ball travel from t = 0 to t = 2 seconds?

128 Ft

What was the average distance traveled for the first two seconds?

64 ft per second

What is another name for this?

average velocity

Draw a line connecting (0, h (0)) and (2, h (2)). What is this line?

secant line

What does the average distance traveled (per second) represent in terms of this line?

slope

Write the equation of this line.

y – 0 = 64(x – 0) or y – 128 = 64(x – 2)

In general, __________________________________, can be found by using the formula: The average rate of change of a function (slope of the secant) Where [a,b] is a closed interval on which f is defined

The equation of ___________________________, can be found by:

1. Finding the slope of the secant (AROC)

2. using point/slope with either point

The secant line

In general, as the interval get smaller (as b gets closer to a ), what line are we approximating?

tangent line

In terms of the original problem, what does this represent?

Instantaneous velocity

In general, how can we represent this?

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Average Rate Of Change And Equations

Average Rate of Change and Equations…

Do Now: The height, in feet, of a ball thrown into the air is modeled by h(t) = - 16t 2 – 96t ,…

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