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The given equation is \( y^2 = 13x \), which represents a parabola.

This is a horizontal parabola because the variable \( y \) is squared and \( x \) is linear. Parabolas of the form \( y^2 = 4px \) open either to the left or right depending on the sign of \( x \)'s coefficient.

- If the coefficient of \( x \) is positive (like in \( y^2 = 13x \)), the parabola opens **to the right**.
- If the coefficient of \( x \) were negative, it would open to the left.

Therefore, the correct answer is **right**.

Would you like more details or have any questions? Here are five related questions to deepen your understanding:

1. How can you identify the direction of a parabola given its equation?
2. What is the significance of the constant \( 13 \) in the equation \( y^2 = 13x \)?
3. How do parabolas differ when the \( x \)-variable is squared instead of the \( y \)-variable?
4. What would the equation of a parabola look like if it opened to the left?
5. How would the equation change if the parabola opened upward or downward?

**Tip:** Always check which variable is squared to determine if the parabola opens horizontally (left or right) or vertically (upward or downward).

What is the opening of the parabola y^2 = 13x?

Understand how to determine the direction of opening for the parabola y^2 = 13x. This question involves key concepts from coordinate geometry and algebra, focusing on how the sign of the coefficient affects the parabola's direction. Suitable for high school students.

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