Help with graphs in algebra 2

Question

specifically number 28 on the June 2016 algebra 2 cc regents but I need help graphing when told the amplitude,period,midline.. I know it's kinda hard to explain on here without a graph

Answer 1

Nat, here's the trick - every sine or cosine graph can look basically the same. You just need to move the axes and points to fit it.

The amplitude is kind of like the absolute value, in that it describes how far up and down it goes from the midline.

Let's say the midline is 3 and the amplitude is 2. Then, your graph will go up to 5 and down to 1.

A period is how long it takes for one cycle of the graph to happen, or where it starts again.

If the period of sine is 2π, with a midline of 0 and an amplitude of 1, the graph starts at (0,0), goes up to (π/2,1), crosses at (π,0), goes down to (3π/2,-1), then crosses again at (2π,0), where it starts over.

Here's the trick I was talking about before. Let's say you read it wrong and the period was actually 4π and the amplitude was 2. Instead of erasing the entire thing, erase the "1" on your y-axis and change it to a 2. Then change the points on your x-axis to π, 2π, 3π and 4π.

If the midline changes, simply move the x-axis and relable your upper and lower points on the y-axis.

Hope this helps!