Practice It

Predict, Observe, Test

Phase & Vertical Shifts in Action

The equation y = A sin(Bx - C) + D represents a transformed sine function. 

A is the amplitude (vertical stretch/compression)

B affects the period (horizontal stretch/compression)

C is the phase shift (horizontal translation)

D is the vertical shift 

Amplitude (A):

The absolute value of A determines the distance from the midline to the maximum or minimum value of the sine wave. If A is negative, the graph is reflected across the midline.

Period (2π/|B|):

The period is the length of one complete cycle of the sine wave. The value of B affects how compressed or stretched the graph is horizontally.

Phase Shift (C/B):

The phase shift determines how much the graph is shifted left or right. A positive C shifts the graph to the right, while a negative C shifts it to the left.

Vertical Shift (D):

The vertical shift determines how much the graph is shifted up or down. A positive D shifts the graph up, and a negative D shifts it down. The line y = D is the midline of the graph.

Checklist

•  I tested each parameter and observed its effect.

• I wrote what each parameter means for a robot.

• I successfully wrote an equation and sketched a graph for the given robot scenarios.

• I correctly decoded the mystery graphs to find their equations

• I justified my reasoning.

• I identified and fixed the errors in all the provided analysis challenges.