Question

analyze the given graph of the parabola. which statements are true? the axis of symmetry is x = 3 the vertex is graph opens downward the axis of symmetry is x = 1

Explanation:

Step1: Identify axis - of - symmetry

The axis of symmetry of a parabola is a vertical line that passes through the vertex. For a parabola, if we can find the vertical line that divides the parabola into two mirror - image halves, we can determine the axis of symmetry. By observing the graph, the vertical line that splits the parabola symmetrically is \(x = 3\).

Step2: Identify the vertex

The vertex of a parabola lies on the axis of symmetry. Since the axis of symmetry is \(x = 3\), and we can see from the graph that the lowest point (for an upward - opening parabola) is on \(x = 3\). Also, the parabola opens upward.

Answer:

The axis of symmetry is \(x = 3\) is true. The vertex is on the axis of symmetry \(x = 3\) and the parabola opens upward, so the statement "The graph opens downward" is false. The axis of symmetry is \(x = 3\) (not \(x=- 1\)). So the true statement is: The axis of symmetry is \(x = 3\).