Quadratic Functions and Parabolas

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Quadratic Function

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A polynomial function of degree 2, generally represented as f(x) = ax^2 + bx + c, where a, b, and c are constants.

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Parabola

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The graph of a quadratic function, which is a U-shaped curve that can open upwards or downwards.

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Vertex of a Parabola

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The highest or lowest point on the graph of a parabola, depending on whether it opens downwards or upwards.

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Vertex Form of a Quadratic Function

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A way to express a quadratic function as f(x) = a(x-h)^2 + k, where (h, k) is the vertex of the parabola.

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Axis of Symmetry

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A vertical line that divides the parabola into two mirror images, passing through the vertex.

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Standard Form of a Quadratic Function

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The expression of a quadratic function as f(x) = ax^2 + bx + c.

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Minimum Value

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The lowest point or value of a parabola when it opens upwards.

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Maximum Value

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The highest point or value of a parabola when it opens downwards.

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Intercept Form of a Quadratic Function

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A way to express a quadratic function as f(x) = a(x-p)(x-q), where p and q are the x-intercepts.

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Discrete Domain

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A set of input values consisting of only certain numbers in an interval.