Question

for the parabola graphed below, identify its vertex, axis of symmetry, and state if it opens downwards.

Explanation:

Step1: Identify the vertex

The vertex of a parabola is the lowest or highest point. From the graph, the vertex is at the point $(- 3,-2)$.

Step2: Determine the axis of symmetry

The axis of symmetry of a parabola is a vertical line passing through the vertex. For a vertex $(h,k)$, the equation of the axis of symmetry is $x = h$. Here, $h=-3$, so the axis of symmetry is $x=-3$.

Step3: Check the opening direction

If the parabola opens upwards, the vertex is the minimum - point; if it opens downwards, the vertex is the maximum - point. Since the vertex $(-3,-2)$ is the minimum point, the parabola opens upwards.

Answer:

Vertex: $(-3,-2)$; Axis of symmetry: $x = - 3$; Opens: Upwards