Question

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

Explanation:

Step1: Recall the definition of axis of symmetry for a parabola

The axis of symmetry of a parabola is a vertical line that divides the parabola into two mirror - image halves. For a parabola in the form \(y = ax^{2}+bx + c\), the formula for the axis of symmetry is \(x=-\frac{b}{2a}\). For a parabola that is symmetric about the \(y\) - axis (where \(b = 0\) in the quadratic function \(y=ax^{2}+bx + c\)), the equation of the axis of symmetry is \(x = 0\). Another way is to observe the graph.

Step2: Analyze the graph

Looking at the given graph of the parabola, we can see that the left - hand side of the parabola is a mirror image of the right - hand side with respect to the \(y\) - axis. The \(y\) - axis is represented by the equation \(x = 0\).

Answer:

\(x = 0\)