Question

the axis of symmetry is x = 5
the vertex
q. which of the following correctly describes the vertex, axis of symmetry, and direction in which the parabola opens, based on the graph shown? select all that are true.
the parabola

Explanation:

Step1: Identify vertex

The vertex of a parabola is the point where the parabola changes direction. From the graph, the vertex is the lowest - point of the parabola. The x - coordinate of the vertex lies on the axis of symmetry. The axis of symmetry is $x = 5$. Looking at the graph, the vertex appears to be at the point where $x = 5$ and $y$ is at its minimum value. Let's assume the vertex is $(5, - 3)$ (by observing the grid).

Step2: Determine axis of symmetry

The axis of symmetry of a parabola is a vertical line that divides the parabola into two mirror - images. For a parabola in the form $y=a(x - h)^2 + k$, the axis of symmetry is $x = h$. Here, from the graph and the given information, the axis of symmetry is $x = 5$.

Step3: Find direction of opening

Since the parabola has a minimum point (the vertex), it opens upwards.

Answer:

Vertex: $(5,-3)$; Axis of symmetry: $x = 5$; Direction of opening: upwards