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.

검증된 단계별 안내

Recall that a parabola is a U-shaped curve described by a quadratic function of the form \(y = ax^2 + bx + c\), where \(a \neq 0\).

If the parabola opens downward, it means the coefficient \(a\) is negative (\(a < 0\)).

The highest point on such a parabola is called the vertex, which represents either the maximum or minimum value of the quadratic function.

For a parabola opening downward, the vertex corresponds to the maximum point on the graph.

Therefore, the highest point on the graph of a parabola that opens down is the \(\textbf{maximum}\) of the parabola.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.