Question

look at this graph: graph of a parabola opening downward with vertex at (0,0) what is the equation of the axis of symmetry?

Explanation:

Step1: Identify the vertex's x - coordinate

The graph is a parabola (a quadratic function graph). The axis of symmetry of a parabola passes through its vertex. From the graph, the vertex of the parabola is at the point \((0, y)\) (where \(y\) is the y - coordinate of the vertex, but we only care about the x - coordinate for the axis of symmetry). The x - coordinate of the vertex is \(0\).

Step2: Determine the equation of the axis of symmetry

For a parabola, the equation of the axis of symmetry is a vertical line (since the parabola opens up or down) in the form \(x = h\), where \(h\) 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:

\(x = 0\)