Polynomial duty whose general form is (f(x) = extrmAx^2 + extrmB x + extrmC), wherein A ≠ 0 and A, B, C ∈ (mathbbR).

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A second-degree polynomial role in which all the coefficients the the terms through a level less than 2 room zeros is called a quadratic function.


Properties

The graph that a second-degree polynomial function has its vertex in ~ the beginning of the Cartesian plane.The zeros that a second-degree polynomial function are offered by the following :If (B2 – 4AC) ≥ 0, the zeros are actual numbers: (x_1 = frac− extrmBspace + space sqrt extrmB^2 − 4 extrmAC2 extrmA) and (x_2 = frac− extrmBspace −space sqrt extrmB^2 − 4 extrmAC2 extrmA);If the duty is that the type f(x) = A(x^2) + B(x), the zeros are : (x_1) = 0 and also (x_2) = − (fracBA);If the duty is that the form f(x) = A(x^2) + C, the zeros room : (x_1) = (sqrt− fracCA) and (x_2) = − (sqrt− fracCA), whereby AC If the role is the the type f(x) = A(x^2), the zeros room : (x_1)= 0 and (x_2)= 0.


Examples

The graphical representation of a second-degree polynomial function defined by the relationship (f(x) = x^2) is a basic parabola.

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The graphical depiction of a second-degree polynomial duty defined through the relationship (f(x) = (x − a)^2) is a straightforward parabola translated horizontally.

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The graphical depiction of the second-degree polynomial function defined through the relationship (f(x) = x^2 + k) is a simple parabola interpreted vertically.

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The graphical representation of the second-degree polynomial role defined by the partnership (f(x) = a(x − h)^2 + k) is a basic parabola translated horizontally and also vertically.

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This graph illustrates the role f identified by f(x) = (left ( x+3 ight )^2 – 4)