Question

You are asked to graph a parabola on a coordinate plane. You are given the information that the focus is located at (3,6) and the directrix is at y=2 . At which point would you graph the vertex on the coordinate plane?(1 point)vertex: (,)

Answer 1

To find the vertex of a parabola given its focus and directrix, we can use the following method:

1. **Identify the focus and directrix**:
- Focus: \( (3, 6) \)
- Directrix: \( y = 2 \)

2. **Determine the vertex's location**:
The vertex lies midway between the focus and the directrix. To find the y-coordinate of the vertex, we take the average of the y-coordinate of the focus and the value of the directrix.

\[
\text{Vertex y-coordinate} = \frac{y_{\text{focus}} + y_{\text{directrix}}}{2} = \frac{6 + 2}{2} = \frac{8}{2} = 4
\]

3. **Vertex x-coordinate**:
The x-coordinate of the vertex will be the same as the x-coordinate of the focus since the parabola opens up or down (not sideways).

\[
\text{Vertex x-coordinate} = x_{\text{focus}} = 3
\]

4. **Combine the coordinates**:
Therefore, the coordinates of the vertex are:

\[
\text{Vertex} = (3, 4)
\]

Hence, the vertex of the parabola is at the point \( (3, 4) \).

**Final answer: vertex: (3, 4)**