Question

for the parabola graphed below, identify its vertex, axis of symmetry, and state if it opens upwards or downwards. the vertex of the parabola is the axis of symmetry is the parabola opens select an answer question help: written example submit question

Explanation:

Step1: Identify vertex

The vertex is the highest or lowest point of the parabola. From the graph, the vertex is at the point $(3,1)$.

Step2: Determine axis of symmetry

The axis of symmetry 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 opening direction

If the parabola has a maximum - point (highest point), it opens downwards. Since the vertex $(3,1)$ is a maximum - point, the parabola opens downwards.

Answer:

The vertex of the parabola is $(3,1)$
The axis of symmetry is $x = 3$
The parabola opens downwards