### Home > INT3 > Chapter 10 > Lesson 10.1.1 > Problem 10-13

Write a possible equation for each graph.

Use the general equation

.

Determine the value for each of the four parameters.Identify a convenient locator point.

In this case, we will use:Since our point is on the midline, we will use the sine function.

The-value of the point also represents the horizontal shift:Next find

, the vertical shift.

The graphhas a midline at(the-axis).

The parameteris the distance that midline is shifted vertically.

In this case.The amplitude (

) is the distance from the midline ( ) to the highest point.

In this caseand the highest point is, so .

Since the graph increases from the locator point in the same waydoes,is positive.You will learn more about the parameter

in future lessons.

For now, know thatsince the distance from the beginning to the end of one cycle is.

See part (a).

Pay careful attention to the scale on the-axis when determiningand.

notice the first cycle of the graph is an inverted sine curve, so the

-value will be negative.See part (a).

See parts (a) and (c).