Question

what is the equation for the axis of symmetry for the function shown on the graph?

Explanation:

Step1: Identify the vertex of the parabola

The axis of symmetry of a parabola passes through its vertex. From the graph, the x - coordinate of the vertex gives the equation of the axis of symmetry. The vertex of the parabola is at the point where the parabola changes direction. For a parabola opening horizontally or vertically, the axis of symmetry is a vertical or horizontal line respectively. In this case, the parabola is vertical and the vertex has an x - value of - 5.

Step2: Write the equation of the axis of symmetry

The equation of a vertical line is of the form $x = a$, where $a$ is the x - coordinate of any point on the line. Since the axis of symmetry passes through the vertex with x - coordinate - 5, the equation of the axis of symmetry is $x=-5$.

Answer:

$x = - 5$