Question

determine the equation of the midline of the following graph.
answer

Explanation:

Step1: Find the maximum and minimum values

From the graph, the maximum value \(y_{max}=-3\) and the minimum value \(y_{min}=-5\).

Step2: Calculate the mid - line

The formula for the mid - line of a sinusoidal function \(y = A\sin(Bx - C)+D\) (or \(y = A\cos(Bx - C)+D\)) is \(y = D\), and \(D=\frac{y_{max}+y_{min}}{2}\).
Substitute \(y_{max}=-3\) and \(y_{min}=-5\) into the formula: \(D=\frac{-3+( - 5)}{2}=\frac{-3 - 5}{2}=\frac{-8}{2}=-4\).
So the equation of the mid - line is \(y=-4\).

Answer:

$y = - 4$