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.
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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 !
Symbolic algebra
ⓘ Hint: This calculator supports symbolic math. You can enter numbers, but also symbols like a, b, pi or even whole math expressions such as (a+b)/2. If you still don't sure how to make your life easier using symbolic algebra check out our another page: Symbolic calculations
What do you want to calculate today?#
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Calculations data  enter values, that you know here#
Function value ($y$) (the function value at single point x, often marked as f(x))  =>  
Function argument ($x$)  <=  
Coefficient before power of two ($a$)  <=  
Coefficient before power of one ($b$)  <=  
Free parameter ($c$)  <= 
Result: function value ($y$)#
Summary  
Used formula  Show source$y= a~{ x}^{2}+ b~ x+ c$  
Result  Show source$3$  
Numerical result  Show source$3$  
Result step by step  
 
Numerical result step by step  

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 upwards,
 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).
 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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