Unit 7, Lesson 14
Amplitude and Midline
Algebra 2
14.1
Warm-up
Comparing Parabolas
Match each equation to its graph. Be prepared to explain how you know which graph belongs with each equation.
A
B
C
D
E
14.2
Activity
Blowing in the Wind
Suppose a windmill has a radius of 1 meter, and the center of the windmill is at
- Write a function describing the relationship between the height,
, of and the angle of rotation, . Explain your reasoning. - Describe how your function and its graph would change if:
- the windmill blade has a length of 3 meters.
- the windmill blade has a length of 0.5 meter.
- Test your predictions using graphing technology.
Student Lesson Summary
Suppose a bike wheel has a radius of 1 foot and we want to determine the height of a point,
The graph of the height of
The horizontal line
What if the wheel had a radius of 11 inches instead? How would that affect the height,
This wheel can also be modeled by a sine function,
The amplitude of the function is the length from the midline to the maximum value, shown here with a dashed line, or, since they are the same, the length from the minimum value to the midline. For the graph of
For the graph of
amplitude
The maximum distance of the values of a periodic function above or below the midline.
midline
The value halfway between the maximum and minimum values of a period function. Also the horizontal line whose
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