https://file.aiquickdraw.com/mathbot/file/1726842218477np7ulr15.jpg

The equation in the problem is:

\[
f(x) = 3(x - 3)^2
\]

You're asked to solve for \(x\) where:

\[
3(x - 3)^2 = 108
\]

### Steps to solve:

1. Divide both sides of the equation by 3:

\[
(x - 3)^2 = \frac{108}{3} = 36
\]

2. Take the square root of both sides:

\[
x - 3 = \pm \sqrt{36} = \pm 6
\]

3. Solve for \(x\):

- \(x - 3 = 6\) gives \(x = 9\)
- \(x - 3 = -6\) gives \(x = -3\)

### Solutions:

- Smaller solution: \(x = -3\)
- Larger solution: \(x = 9\)

Let me know if you need further clarification or details.

Here are some additional questions to expand your understanding:

1. What is the general form of a quadratic function and how does it differ from this one?
2. How does the transformation \(x - 3\) shift the graph of \(f(x)\)?
3. What is the effect of multiplying the quadratic term by 3 in this function?
4. How can you check your solutions by substituting them back into the equation?
5. What does the graph of this function look like and where do the solutions correspond on the graph?

**Tip**: Always verify solutions to quadratic equations by substituting them back into the original equation.

Graph the quadratic function using a graphing utility: f(x) = 3(x - 3)^2. Use the graph to find the solutions to 3(x - 3)^2 = 108.

Learn how to solve and graph the quadratic equation 3(x - 3)^2 = 108 using algebraic methods. The problem includes concepts of quadratic equations and graphing functions. Suitable for high school students in Grades 9-11.

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