Question

what are the vertex and the axis of symmetry of the parabola shown in the diagram below? the vertex is (-1, 0), and the axis of symmetry is x = -1. the vertex is (0, -1), and the axis of symmetry is x = 0. the vertex is (-1, 0), and the axis of symmetry is y = 0. the vertex is (0, -1), and the axis of symmetry is y = -1.

Explanation:

Step1: Identify the vertex

The vertex of a parabola is the point where the parabola changes direction. Looking at the graph, the lowest - point (since the parabola opens upwards) is at the point where \(x = 0\) and \(y=-1\). So the vertex is \((0, - 1)\).

Step2: Identify the axis of symmetry

The axis of symmetry of a parabola is a vertical line that passes through the vertex. For a parabola, the equation of a vertical line is of the form \(x = a\), where \(a\) is the \(x\) - coordinate of the vertex. Since the \(x\) - coordinate of the vertex is \(0\), the equation of the axis of symmetry is \(x = 0\).

Answer:

The vertex is \((0, - 1)\), and the axis of symmetry is \(x = 0\). So the correct option is: The vertex is \((0, - 1)\), and the axis of symmetry is \(x = 0\).