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.

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

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.

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