Question

state the equation of the axis of symmetry and vertex of the parabola shown on the graph. state the equation of the axis of symmetry: state the vertex of the parabola as an ordered pair.

Explanation:

Step1: Identify vertex

The vertex of a parabola is the lowest (or highest) point. From the graph, the vertex is at the point where $x = - 5$ and $y=4$. So the vertex is $(-5,4)$.

Step2: Determine axis of symmetry

The axis of symmetry of a parabola passes through the vertex. For a parabola opening up - or down - ward, the equation of the axis of symmetry is of the form $x = a$, where $a$ is the $x$ - coordinate of the vertex. Since the $x$ - coordinate of the vertex is $-5$, the equation of the axis of symmetry is $x=-5$.

Answer:

Equation of the axis of symmetry: $x = - 5$
Vertex: $(-5,4)$