Questions: Based on the graph above, determine the amplitude, midline, and period of the function

Based on the graph above, determine the amplitude, midline, and period of the function
Transcript text: Based on the graph above, determine the amplitude, midline, and period of the function
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Solution

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Solution Steps

Step 1: Find the amplitude

The amplitude is the distance from the midline to the highest or lowest point of the graph. The highest point is at y = 2, and the lowest is at y = -8. The midline is halfway between these, at y = -3. Therefore, the amplitude is 2 - (-3) = 5.

Step 2: Find the midline

The midline is the horizontal line that passes exactly between the highest and lowest points of the graph. The highest y-value is 2 and the lowest y-value is -8. The midline is the average of these values: (2 + (-8))/2 = -3. Thus, the midline is y = -3.

Step 3: Find the period

The period is the horizontal distance it takes for the graph to complete one full cycle. Starting at x = -2, where the graph is at its maximum, it returns to a maximum at x = 2. Thus, the period is 2 - (-2) = 4.

Final Answer

Amplitude: 5, Midline: y = -3, Period: 4

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