Fill in the blank(s) to correctly complete each sentence. The highest point on the graph of a parabola that opens down is the ____ of the parabola.

Verified step by step guidance

1. Recall that a parabola is a U-shaped curve described by a quadratic function of the form \(y = ax^2 + bx + c\), where \(a \neq 0\).
2. If the parabola opens downward, it means the coefficient \(a\) is negative (\(a < 0\)).
3. The highest point on such a parabola is called the vertex, which represents either the maximum or minimum value of the quadratic function.
4. For a parabola opening downward, the vertex corresponds to the maximum point on the graph.
5. Therefore, the highest point on the graph of a parabola that opens down is the \textbf{maximum} of the parabola.

Key Concepts

Parabola

A parabola is a U-shaped curve that is the graph of a quadratic function. It can open upwards or downwards depending on the sign of the leading coefficient in the quadratic equation.

Vertex of a Parabola

The vertex is the highest or lowest point on the graph of a parabola. For a parabola that opens downwards, the vertex represents the maximum point.

Maximum and Minimum Values

In quadratic functions, the vertex corresponds to either a maximum or minimum value. If the parabola opens down, the vertex is the maximum; if it opens up, the vertex is the minimum.