Question

what is the axis of symmetry for this quadratic function?

Explanation:

Step1: Recall axis of symmetry for parabola

The axis of symmetry of a parabola (quadratic function) is a vertical line that passes through the vertex, dividing the parabola into two mirror - image halves. For a parabola that is symmetric about the y - axis (the line \(x = 0\)), we can observe the graph.

Step2: Analyze the given graph

Looking at the graph of the quadratic function (a parabola), we can see that the parabola is symmetric with respect to the y - axis. The y - axis is represented by the equation \(x=0\). We can check the points on the parabola. For example, if we take a point \((x,y)\) on the parabola, the point \((-x,y)\) is also on the parabola, which is the property of a graph symmetric about the \(x = 0\) (y - axis) line.

Answer:

The axis of symmetry for the given quadratic function is the line \(x = 0\) (the y - axis).