# Question #e7f98

##### 1 Answer

**y = 3(1/4(x - 3 #pi#/2)) - 4**

#### Explanation:

Consider this skeleton equation:

**y = a(bx + c) + d**

Amplitude is the **a** value, so plug it in for **a** in the equation:

**y = 3(bx + c) + d**

With the period you can find the **b** value using this equation:

**period = 2 #pi#/b**

(use 2

Since you already know the period, plug it in to this equation and solve for

**b**:

**8**#pi# = 2#pi# /b ---> b = 1/4

Now plug this

**b**value into the skeleton equation:

**y = 3(1/4(x + c)) + d**

Phase shift of 3**c** value; now plug it into the equation:

**y = 3(1/4(x - 3 #pi#/2)) + d**

Finally, the vertical shift of -4 is shifting the graph downward, which is the **d** value. Now plug it into the equation to get the final equation:

**y = 3(1/4(x - 3 #pi#/2)) - 4**