Polynomial role whose general type is \(f(x) = \textrmAx^2 + \textrmB x + \textrmC\), where A ≠ 0 and also A, B, C ∈ \(\mathbbR\).

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A second-degree polynomial duty in which all the coefficients the the terms with a degree less than 2 space zeros is called a quadratic function.


Properties

The graph that a second-degree polynomial function has that vertex in ~ the beginning of the Cartesian plane.The zeros the a second-degree polynomial function are given by the complying with :If (B2 – 4AC) ≥ 0, the zeros are genuine numbers: \(x_1 = \frac−\textrmB\space + \space \sqrt\textrmB^2 − 4\textrmAC2\textrmA\) and \(x_2 = \frac−\textrmB\space −\space \sqrt \textrmB^2 − 4\textrmAC2\textrmA\);If the role is that the form f(x) = A\(x^2\) + B\(x\), the zeros are : \(x_1\) = 0 and also \(x_2\) = − \(\fracBA\);If the function is of the type f(x) = A\(x^2\) + C, the zeros are : \(x_1\) = \(\sqrt− \fracCA\) and \(x_2\) = − \(\sqrt− \fracCA\), where AC If the duty is that the kind f(x) = A\(x^2\), the zeros are : \(x_1\)= 0 and \(x_2\)= 0.


Examples

The graphical depiction of a second-degree polynomial function defined through the relationship \(f(x) = x^2\) is a an easy parabola.

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The graphical representation of a second-degree polynomial role defined through the connection \(f(x) = (x − a)^2\) is a simple parabola analyzed horizontally.

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The graphical representation of the second-degree polynomial function defined by the connection \(f(x) = x^2 + k\) is a basic parabola translated vertically.

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The graphical depiction of the second-degree polynomial duty defined by the relationship \(f(x) = a(x − h)^2 + k\) is a straightforward parabola interpreted horizontally and also vertically.

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This graph illustrates the duty f identified by f(x) = \(\left ( x+3 \right )^2 – 4\)