Question

what is the equation for the axis of symmetry for the function shown on the graph? a ( x = 1 ) b ( y = 1 ) c ( x = -1 ) d ( y = -1 )

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. The equation of a vertical line is of the form \(x = h\), where \(h\) is the x - coordinate of the vertex. So we can eliminate options B (\(y = 1\)) and D (\(y=-1\)) since they are horizontal lines, and the axis of symmetry of a parabola (opening up or down) is vertical.

Step2: Determine the x - coordinate of the vertex from the graph

Looking at the graph of the parabola, the vertex (the highest point of the parabola, since it opens downwards) lies at \(x = 1\) (by observing the grid, the vertex is at the point where \(x = 1\) on the x - axis). So the equation of the axis of symmetry is \(x=1\).

Answer:

A. \(x = 1\)