Question

look at this graph:
what is the equation of the axis of symmetry?
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Explanation:

Step1: Identify the graph type

The graph is a parabola (U - shaped), opening upwards, with vertex at the origin \((0,0)\).

Step2: Recall axis of symmetry for parabola

For a parabola in the form \(y = ax^{2}+bx + c\), the axis of symmetry is given by the formula \(x=-\frac{b}{2a}\). For the parabola \(y = ax^{2}\) (since vertex is at \((0,0)\), \(b = 0\) and \(c=0\)), substituting \(b = 0\) into the formula \(x=-\frac{b}{2a}\), we get \(x = 0\). Also, visually, the parabola is symmetric about the \(y\) - axis (the line \(x = 0\)) as the left and right halves of the parabola are mirror images with respect to the \(y\) - axis.

Answer:

\(x = 0\)