$f$ is a trigonometric function of the form $f(x)=a \cos (b x+c)+d$.
Below is the graph of $f(x)$. The function has a maximum point at $(-2,-3)$ and a minimum point at $(-2.5,-9)$. Find a formula for $f(x)$. Give an exact expression.

Please directly answer the question and provide the final value, e.g., 1, 2.5, 300.
Question: $f$ is a trigonometric function of the form $f(x)=a \cos (b x+c)+d$.
Below is the graph of $f(x)$. The function has a maximum point at $(-2,-3)$ and a minimum point at $(-2.5,-9)$. Find a formula for $f(x)$. Give an exact expression.

Please first conduct reasoning, and then answer the question and provide the final value, e.g., 1, 2.5, 300, at the end.
Question: $f$ is a trigonometric function of the form $f(x)=a \cos (b x+c)+d$.
Below is the graph of $f(x)$. The function has a maximum point at $(-2,-3)$ and a minimum point at $(-2.5,-9)$. Find a formula for $f(x)$. Give an exact expression.
