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The equation you're asked to write is in the vertex form of a parabola, which is generally written as:

\[
f(x) = a(x - h)^2 + k
\]

Where:
- \( a \) is the same coefficient as the original function \( f(x) = 3x^2 \), so \( a = 3 \).
- \( (h, k) \) is the vertex of the parabola, given here as \( (3, -2) \).

Substituting \( a = 3 \), \( h = 3 \), and \( k = -2 \) into the vertex form equation, we get:

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

So the equation of the parabola in vertex form is:

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

Would you like further details or have any questions on how this was derived?

Here are some related questions:
1. How do you convert a quadratic equation from standard form to vertex form?
2. What does the "a" value tell us about the shape of the parabola?
3. How do we find the vertex of a parabola given in standard form?
4. What happens to the graph of \( f(x) \) if \( a \) becomes negative?
5. Can you describe the geometric significance of the vertex in relation to the graph?

**Tip:** In the vertex form, the vertex \((h, k)\) indicates the highest or lowest point of the parabola, and adjusting \( a \) changes the "width" and direction (upward or downward).

Write an equation in vertex form of the parabola that has the same shape as the graph of f(x) = 3x^2, but with the point (3, -2) as the vertex.

Learn how to write a quadratic equation in vertex form with the same shape as f(x) = 3x^2, but with a different vertex (3, -2). This involves understanding the vertex form of a parabola and applying key algebraic concepts. Suitable for Grades 9-12.

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