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To determine which parabola has a vertex at \( (0, 3) \) and opens to the right, we need to understand the standard form of a parabola that opens horizontally (to the left or right).

For a parabola that opens to the right, the equation typically takes the form:

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

where \( (h, k) \) is the vertex of the parabola, and if \( a > 0 \), it opens to the right.

Given that the vertex is \( (0, 3) \), the equation becomes:

\[
x = a(y - 3)^2
\]

Now, looking at the answer choices, the one that fits this form is:

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

This is the equation of the parabola that has a vertex at \( (0, 3) \) and opens to the right.

### The correct answer is: 
**\( x = (y - 3)^2 \)**

Would you like further explanation on any step? Here are a few related questions to explore:

1. How do we determine the direction a parabola opens based on its equation?
2. What is the difference between parabolas that open vertically and those that open horizontally?
3. How can you tell if a parabola opens to the left or right?
4. How do transformations affect the vertex of a parabola?
5. What happens to the shape of a parabola as the value of \( a \) changes?

**Tip:** For horizontal parabolas, the equation involves \( x \) as a function of \( y \), while for vertical parabolas, \( y \) is a function of \( x \).

Which parabola has a vertex at (0, 3) and opens to the right?

This problem explains how to determine the equation of a parabola with vertex at (0, 3) that opens to the right. It covers the vertex form of a parabola and explores the relationship between the equation and the direction in which it opens. Suitable for high school students in Grades 9-12.

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