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### Equation of the Parabola:
The equation given is \( y^2 = 8x \). This is a horizontal parabola (because \( y^2 \) is on the left side), and it's in the form \( y^2 = 4px \) where \( p \) is the distance from the vertex to the focus.

### 15. What is the vertex?
- For the equation \( y^2 = 8x \), the vertex is at the origin \( (0, 0) \).
  - **Answer:** A. \( (0, 0) \)

### 16. What is the axis of symmetry?
- The axis of symmetry is the line that passes through the vertex and is parallel to the direction in which the parabola opens. Since this is a horizontal parabola, the axis of symmetry is the x-axis.
  - **Answer:** B. \( y = 0 \)

### 17. Describe the opening of the parabola:
- For the equation \( y^2 = 8x \), the parabola opens to the right.
  - **Answer:** C. Rightward

### 18. What is the equation of the directrix?
- The distance \( p \) is \( p = \frac{8}{4} = 2 \). The directrix is a vertical line \( x = -p \), so here it is \( x = -2 \).
  - **Answer:** D. \( x = -2 \)

### 19. Which of the following is the vertex of the parabola \( (x + 2)^2 = 12(y - 5) \)?
- To find the vertex, convert the equation to the form \( (x - h)^2 = 4p(y - k) \). Here, \( h = -2 \) and \( k = 5 \), so the vertex is \( (-2, 5) \).
  - **Answer:** C. \( (-2, 5) \)

### 20. What is the equation of the directrix of the parabola \( (x + 2)^2 = 12(y - 5) \)?
- First, find \( p \) from \( 4p = 12 \), so \( p = 3 \). The directrix for a vertical parabola is \( y = k - p \). So, \( y = 5 - 3 = 2 \).
  - **Answer:** A. \( y = 2 \)

Would you like further explanations on any of these answers or a breakdown of the steps?

### Follow-Up Questions:
1. How do you derive the equation of the directrix for any parabola?
2. What is the general form of a parabola, and how can it be transformed?
3. How does the vertex form of a parabola help in graphing?
4. Can you determine the focus of the parabola \( y^2 = 8x \)?
5. What is the relationship between the directrix and the focus in a parabola?

**Tip:** Remember that the sign of the \( x^2 \) or \( y^2 \) term in the parabola's equation tells you whether the parabola opens up/down or left/right.

For item numbers 15 - 20, refer to the following equation of a parabola: y^2 = 8x. Solve questions regarding vertex, axis of symmetry, direction of opening, and directrix.

Explore the solutions to questions involving the parabola y^2 = 8x. This problem covers key concepts such as finding the vertex, axis of symmetry, direction of opening, and equation of the directrix, suitable for students in Grades 9-10.

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