Question

Identify the vertex and axis of symmetry of the parabola with the given points (0, 50), (-20, 50), and (-10, 0)

Answer 1

To identify the vertex and axis of symmetry of the parabola defined by the points (0, 50), (-20, 50), and (-10, 0), we can follow these steps:

1. **Determine the shape of the parabola**: We note two points on the parabola, (0, 50) and (-20, 50), both of which have the same \(y\) value. This indicates that these points are symmetrical about the axis of symmetry. The third point (-10, 0) is the lowest point if the parabola opens upward or the highest if it opens downward, but we will confirm this based on the minimum \(y\) value.

2. **Finding the axis of symmetry**: The axis of symmetry will be midway between the points (0, 50) and (-20, 50). The \(x\) coordinate of the axis can be found as follows:

\[
x = \frac{-20 + 0}{2} = -10
\]

Thus, the axis of symmetry is \(x = -10\).

3. **Identifying the vertex**: Since (-10, 0) is a point on the parabola and is directly on the axis of symmetry we determined, this point is also the vertex of the parabola.

So, we have:
- **Vertex**: \((-10, 0)\)
- **Axis of Symmetry**: \(x = -10\)

In conclusion, the vertex of the parabola is (-10, 0), and its axis of symmetry is \(x = -10\).