Question

determining the vertex of a parabola from its graph
what is the vertex of the parabola in the graph?
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Explanation:

Step1: Recall the vertex definition

The vertex of a parabola is the minimum (for upward - opening) or maximum (for downward - opening) point. For a parabola, it's also the point on the axis of symmetry.

Step2: Identify the axis of symmetry

Looking at the graph, the parabola is symmetric about the vertical line that is midway between the two x - intercepts. The x - intercepts are at \(x=-5\) and \(x = - 1\) (wait, no, looking at the grid, the two x - intercepts are at \(x=-5\)? Wait, no, the points on the x - axis are at \(x=-5\) (left) and \(x=-1\) (right)? Wait, no, looking at the grid, the left x - intercept is at \(x=-5\)? Wait, no, the graph has points on the x - axis: one at \(x=-5\) (when x=-5, y = 0) and one at \(x=-1\) (when x=-1, y = 0). The axis of symmetry is the vertical line \(x=\frac{-5+( - 1)}{2}=\frac{-6}{2}=-3\).

Step3: Find the y - coordinate of the vertex

Looking at the graph, when \(x=-3\), the y - coordinate of the vertex is \(-4\). So the vertex is at \((-3,-4)\).

Answer:

\((-3, - 4)\)