Quadratic Functions

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A polynomial function of degree 2, often written in the form f(x) = ax² + bx + c, where a, b, and c are constants, and a ≠ 0.

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Quadratic Function

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Vertex

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Axis of Symmetry

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Standard Form

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Vertex Form

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Factored Form

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The U-shaped graph of a quadratic function. The direction of its opening depends on the sign of the coefficient a.

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Parabola

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The values of x that make the quadratic function equal to zero f(x) = 0. These are the x-intercepts of the graph.

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Roots, Zeros, or Solutions

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Discriminant

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The set of all possible output values (y) of a quadratic function, determined by the direction the parabola opens and its vertex. (y ≥ min or y ≤ max).

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Range