### Home > PC3 > Chapter 8 > Lesson 8.1.2 > Problem8-34

8-34.

Lauren is playing with a yo-yo and keeping track of its height over time. She has plotted some key points on the graph at right. The $y$‑values are in inches and the $x$‑values are in seconds. Complete the following problems based on the graph. Homework Help ✎

1. How much time does it take to complete one cycle?

2. How long is the string?

3. Write an equation that models the height of the yo-yo over time.

4. Determine the first two times when the yo-yo is exactly $30$ inches above the ground.

Use the x-values to determine this quantity.

This is the difference in the maximum and minimum heights.

Identify:
1. Amplitude
2. Vertical Shift
3. Horizontal Shift
4. b (frequency)

Note: Part (a) is the period and b = 2π<\i>/p
Test your answer in your graphing calculator.

Use a graphing calculator to determine where the function crosses y = 30.
Note: The first two times may have occurred before the curve in the given sketch.