The given equation is \( y^2 = 12x \). This is a quadratic equation in \( y \) and represents a **parabola**.

### Solution:

1. **Rewrite the equation** in a more standard form for a parabola:

   \[
   y^2 = 12x
   \]

   This equation is of the form \( y^2 = 4ax \), where \( a = 3 \) (since \( 4a = 12 \)). The parabola opens to the right because the coefficient of \( x \) is positive.

2. **Vertex:** The vertex of this parabola is at \( (0, 0) \).

3. **Focus and Directrix:**
   - The focus of the parabola is at \( (a, 0) = (3, 0) \).
   - The directrix is the line \( x = -3 \).

4. **Axis of symmetry:** The axis of symmetry is the x-axis (horizontal line \( y = 0 \)).

### Sketch of the Parabola:
- The parabola opens to the right.
- It passes through points such as \( (3, 6) \), \( (3, -6) \), \( (12, 12) \), and \( (12, -12) \).

### Steps to Sketch:
1. **Plot the vertex** at \( (0, 0) \).
2. **Plot the focus** at \( (3, 0) \).
3. Draw the **directrix** line at \( x = -3 \).
4. Sketch the curve such that it opens to the right and approaches the focus, with the axis of symmetry being the x-axis.

If you need a graphical visualization, let me know, and I can create it for you.

### Related Questions:
1. What are the properties of parabolas?
2. How do you find the vertex form of a parabola?
3. What is the equation of a parabola that opens leftward or downward?
4. How does changing the value of \( a \) affect the shape of a parabola?
5. How can the focus and directrix be used to derive the equation of a parabola?

### Tip:
When sketching parabolas, remember that the distance from any point on the parabola to the focus is equal to the distance from that point to the directrix.

Explore how to sketch and solve the quadratic equation y^2 = 12x, which forms a parabola opening to the right. Learn about its vertex, focus, directrix, and sketching steps with a detailed explanation. Suitable for high school students.

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