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## Algebra 2

### Course: Algebra 2>Unit 11

Lesson 6: Amplitude, midline and period

# Midline, amplitude, and period review

Review the basic features of sinusoidal functions: midline, amplitude, and period.

## What are midline, amplitude, and period?

Midline, amplitude, and period are three features of sinusoidal graphs.
start color #ed5fa6, start text, M, i, d, l, i, n, e, end text, end color #ed5fa6 is the horizontal line that passes exactly in the middle between the graph's maximum and minimum points.
start color #1fab54, start text, A, m, p, l, i, t, u, d, e, end text, end color #1fab54 is the vertical distance between the midline and one of the extremum points.
start color #aa87ff, start text, P, e, r, i, o, d, end text, end color #aa87ff is the distance between two consecutive maximum points, or two consecutive minimum points (these distances must be equal).

## Finding features from graph

Given the graph of a sinusoidal function, we can analyze it to find the midline, amplitude, and period. Consider, for example, the following graph.
It has a maximum point at left parenthesis, 1, comma, 7, right parenthesis, then a minimum point at left parenthesis, 3, comma, 3, right parenthesis, then another maximum point at left parenthesis, 5, comma, 7, right parenthesis.
The horizontal line that passes exactly between y, equals, 7 (the maximum value) and y, equals, 3 (the minimum value) is start color #ed5fa6, y, equals, 5, end color #ed5fa6, so that's the midline.
The vertical distance between the midline and any of the extremum points is start color #1fab54, 2, end color #1fab54, so that's the amplitude.
The distance between the two consecutive maximum points is start color #aa87ff, 4, end color #aa87ff, so that's the period.
Problem 1
• Current
What is the midline equation?
y, equals

Want to try more problems like this? Check out these exercises: