the graph shows a parabola. what is the equation of its axis of symmetry?

Explanation:

Step1: Recall axis - symmetry property

For a parabola in the form (y = ax^{2}+bx + c), the axis of symmetry is a vertical line (x = h), where for a parabola, the axis of symmetry passes through the vertex.

Step2: Locate the vertex

By observing the graph, the vertex of the parabola is at the point ((1,- 8)).

Step3: Determine the axis - symmetry equation

Since the axis of symmetry of a parabola is a vertical line (x=h) and (h = 1) (x - coordinate of the vertex), the equation of the axis of symmetry is (x = 1).

Answer:

(x = 1)