Question

look at this graph:
graph of a parabola opening upwards with vertex near (-3, -2) and y-intercept near (0, 8)
what is the equation of the axis of symmetry?
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Explanation:

Step1: Identify the parabola's vertex x - coordinate

The graph is a parabola (quadratic function) opening upwards. The axis of symmetry of a parabola is a vertical line that passes through its vertex. From the graph, the vertex of the parabola lies on the x - axis at \(x=-3\) (by observing the grid, the minimum point of the parabola is at \(x = - 3\), \(y\) value around - 2 or so, but for the axis of symmetry, we care about the x - coordinate of the vertex).

Step2: Determine the equation of the axis of symmetry

For a vertical line (axis of symmetry of a parabola), the equation is of the form \(x = h\), where \(h\) is the x - coordinate of the vertex. Since the vertex has an x - coordinate of \(-3\), the equation of the axis of symmetry is \(x=-3\).

Answer:

\(x = - 3\)