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The vertex is a fundamental feature of a quadratic function (a parabola). It represents the highest or lowest point on the graph, depending on the direction of its concavity.

In the given function, f(x)=-(x+5)^{2}, the vertex form of a parabola is f(x) = a(x-h)^2 + k, where (h, k) indicates the vertex.

In our function, (h, k) corresponds to (-5, 0). This means the vertex is located at (-5, 0). Knowing the vertex helps us understand the graph's position and direction.

The axis of symmetry is a vertical line that divides the parabolic graph into two mirror-image halves. It always passes through the vertex.

For a function in the form f(x) = a(x-h)^2 + k, the vertex's x-coordinate (h) determines the axis of symmetry.

In our specific function, f(x)=-(x+5)^{2}, the axis of symmetry can be read directly as x = -5. This vertical line helps maintain the symmetrical nature of the parabola.

Concavity tells us the direction in which a parabola opens. It can be either concave up (opening upwards) or concave down (opening downwards).

The concavity of a quadratic function is determined by the sign of the coefficient a in front of the squared term. For the function f(x)=-(x+5)^{2}, a = -1, which is less than zero.

This negative value indicates that the graph is concave down. Thus, our parabola opens downward with the vertex being the highest point on the graph.

Graphing a parabola involves plotting its vertex and understanding its axis of symmetry and concavity. These characteristics give us the complete shape of the parabola.

For the function f(x)=-(x+5)^{2}, we start by plotting its vertex at (-5, 0). Given the concavity (concave down), the parabola opens downward with this vertex as the highest point.

The axis of symmetry (x = -5) ensures the graph is symmetric about this vertical line. Sketch the curve ensuring it opens downwards from the vertex.

And there you have it! A complete and correct graph of the given quadratic function.