Question

The vertex is (3,-9) the lesser zero is (0,0) the other zero is (6,0) on a graph what would line of symmetry be and the y intercept

Answer 1

To find the line of symmetry and the y-intercept of a quadratic graph given the vertex and the zeros, we can follow these steps:

1. **Vertex**: The vertex given is (3, -9).

2. **Zeros**: The zeros are given as (0, 0) and (6, 0).

### Line of Symmetry

The line of symmetry for a quadratic function \(y = ax^2 + bx + c\) is given by the formula:

\[
x = \frac{x_1 + x_2}{2}
\]

where \(x_1\) and \(x_2\) are the x-coordinates of the zeros.

In this case:
- \(x_1 = 0\) (first zero)
- \(x_2 = 6\) (second zero)

Calculating the line of symmetry:

\[
x = \frac{0 + 6}{2} = \frac{6}{2} = 3
\]

So, the line of symmetry is \(x = 3\).

### Y-Intercept

The y-intercept of a quadratic function is the point where the graph intersects the y-axis. It's typically found by setting \(x = 0\).

From the given information, one of the zeros is already at the y-intercept (0, 0). However, if needed, you can always determine the y-intercept explicitly by substituting \(x = 0\) into the quadratic function if you know its equation. Since we do not have the equation of the parabola from the information provided, we can conclude that the y-intercept is \(y = 0\) at the point (0, 0).

### Summary

- **Line of Symmetry**: \(x = 3\)
- **Y-Intercept**: (0, 0)