# Midline, amplitude, and period review

CCSS Math: HSF.IF.C.7, HSF.IF.C.7e

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.

$\maroonC{\text{Midline}}$ is the horizontal line that passes exactly in the middle between the graph's maximum and minimum points.

$\greenD{\text{Amplitude}}$ is the vertical distance between the midline and one of the extremum points.

$\purpleC{\text{Period}}$ is the distance between two consecutive maximum points, or two consecutive minimum points (these distances must be equal).

*Want to learn more about midline, amplitude, and period? Check out this video.*

## 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 $(1,7)$, then a minimum point at $(3,3)$, then another maximum point at $(5,7)$.

The horizontal line that passes exactly between $y=7$ (the maximum value) and $y=3$ (the minimum value) is $\maroonC{y=5}$, so that's the midline.

The vertical distance between the midline and any of the extremum points is $\greenD2$, so that's the amplitude.

The distance between the two consecutive maximum points is $\purpleC4$, so that's the period.

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