# Beta version

BETA TEST VERSION OF THIS ITEM

This online calculator is currently under heavy development. It may or it may NOT work correctly.

You CAN try to use it. You CAN even get the proper results.

However, please VERIFY all results on your own, as the level of completion of this item is NOT CONFIRMED.

Feel free to send any ideas and comments !

This online calculator is currently under heavy development. It may or it may NOT work correctly.

You CAN try to use it. You CAN even get the proper results.

However, please VERIFY all results on your own, as the level of completion of this item is NOT CONFIRMED.

Feel free to send any ideas and comments !

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# Some facts

- The
**quadratic function**is a function that can be prepresented in the form:

$y= a~{ x}^{2}+ b~ x+ c$where:

**$y$**- function value (the function value at single point x, often marked as f(x)),**$x$**- function argument (called also independent value),**$a$**,**$b$**,**$c$**- quadratic function coefficients (numbers just before x^{2}, x and free parameter).

- The graph of the quadratic function is
**parabola**. Depending on the coefficient value at the second power (a), the following scenarios are possible:

- when the coefficient on the second power is positive (a> 0) - the parabola's arms are directed
**upwards**,

- when the coefficient on the second power is negative (a < 0) - the parabola arms are directed
**downwards**,

- in the case when the coefficient on the second power is equal to zero (a = 0) - the quadratic function reduces to linear function.

- when the coefficient on the second power is positive (a> 0) - the parabola's arms are directed
- A square function can have
**one**,**two**, or**have no zero points**. To check the number of zero places (sometimes also called roots), we can calculate the**discriminant of a quadratic function**(colloquially called delta):

$\Delta={ b}^{2}-4~ a~ c$where:

**$\Delta$**- dicriminant of the quadratic function,**$a$**,**$b$**,**$c$**- quadratic function coefficients (numbers just before x^{2}, x and free parameter).

then the following scenarios are possible:

**discriminant is negative**(Δ <0) - the function**has no roots**, the graph of the function is a parabola, which is located entirety**above the OX axis**or**under the OX axis**,

**discriminant is equal to zero**(Δ = 0) - the function has exactly**one root**, the graph of the function is a parabola whose**vertex lies on the OX axis**:

$h=\frac{- b}{2~ a}$**discriminant is positive**(Δ> 0) - the function has**two different roots**, the function graph is a parabola, whose**arms cross the OX axis**:

$x_1=\frac{- b-\sqrt{ \Delta}}{2~ a}$$x_2=\frac{- b+\sqrt{ \Delta}}{2~ a}$

- A quadratic function is a special case of
**polynomial function**in which the order is 2.

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