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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 !
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Various forms of function formulas
Name  Formula  Legend 
Exponential function in general form  Show source$y={ a}^{ x}$ 

Exponential function with base e (often written as exp(x))  Show source$exp(x)={ e}^{ x}$ 

Homographic function in general form  Show source$y=\frac{ a~ x+ b}{ c~ x+ d}$ 

Function b/x  Show source$y=\frac{ b}{ x}$ 

Linear function in slopeintercept form  Show source$y= a~ x+ b$ 

Linear function in pointslope form  Show source$y=\mathrm{a}\left( x x_0\right)+ y_0$ 

Linear function in constantslope form  Show source$\frac{y  y_0}{x  x_0} = \frac{y_1  y_0}{x_1  x_0}$ 

Zero of the linear function from constantslope form  Show source$x=\frac{ y_0\cdot\left( x_1 x_0\right)}{ y_1 y_0}+ x_0$ 

Quadratic function in standard form  Show source$y= a~{ x}^{2}+ b~ x+ c$ 

Quadratic function in factored form  Show source$y=\mathrm{a}\left( x x_1\right)~\left( x x_2\right)$ 

Quadratic function in vertex form  Show source$y={\mathrm{a}\left( x h\right)}^{2}+ k$ 

Slope of the line
Name  Formula  Legend 
Slope from two points lying on the line  Show source$a=\frac{ y_1 y_0}{ x_1 x_0}$ 

Slope from one point lying on the line (free parameter is needed)  Show source$a=\frac{ y_0 b}{ x_0}$ 

Zeroes of the function (roots)
Name  Formula  Legend 
Zero point of homographic function  Show source$x=\frac{ b}{ a}$ 

Zero of the linear function  Show source$x=\frac{ b}{ a}$ 

Zero of the linear function from pointslope form  Show source$x= x_0\frac{ y_0}{ a}$ 

Zero of the linear function from constantslope form  Show source$x=\frac{ y_0\cdot\left( x_1 x_0\right)}{ y_1 y_0}+ x_0$ 

The first root of the quadratic function  Show source$x_1=\frac{ b\sqrt{ \Delta}}{2~ a}$ 

The second root of the quadratic function  Show source$x_2=\frac{ b+\sqrt{ \Delta}}{2~ a}$ 

Some facts
 The linear function is a function that can be presented in the following form:
$y= a~ x+ b$where:
 $y$  function value (the function value at single point x, often marked as f(x)),
 $x$  function argument (called also independent value),
 $a$, $b$  linear function coefficients (slope and free parameter).
 The graph of the linear function is a straight line.
 Slope of a linear function defines the degree of slope of the line to the OX axis ("horizontal"). Depending on the slope value, we can distinguish three cases:
 when the slope is zero (a = 0)  the function is reduced to the constant function, its plot is a line parallel to the OX axis,
 when the slope is positive (a > 0)  the function is increasing, it's plot is a line going towards the upper right corner of the graph,
 when the slope is negative (a < 0)  the function is decreasing, its plot is a line going towards the lower right corner of the graph.
 when the slope is zero (a = 0)  the function is reduced to the constant function, its plot is a line parallel to the OX axis,
 A linear function can have one, infinitely many or no zeros (roots). This depends on the parameter values a and b as follow:
 when the slope a is different from zero (a ≠ 0)  the function has exactly one root (zero point), the plot of the function crosses the OX axis one time in the point:
$x=\frac{ b}{ a}$  when the slope a is zero, but the free parameter b is not (a = 0 and b ≠ 0)  function has no roots (zero points), it's plot does not cross the OX axis, the function is reduced to the form:
$y = b$  if both the slope a and the free parameter b are zero (a = 0 and b = 0)  the function has infinite number of roots (zero points), it's plot coincides with the axis OX:
$y = 0$
 when the slope a is different from zero (a ≠ 0)  the function has exactly one root (zero point), the plot of the function crosses the OX axis one time in the point:
 The linear function is a special case of the polynomial function with the order of 0 (when a = 0) or 1.
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