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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.
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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$y={\mathrm{a}\left( x h\right)}^{2}+ k$ 

Function discriminant#
Name  Formula  Legend 
Discriminant of homographic function  Show source$D= a\cdot d b\cdot c$ 

Discriminant of the quadratic function  Show source$\Delta={ b}^{2}4~ a~ c$ 

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

Parabola vertex#
Name  Formula  Legend 
The x coordinate of parabola vertex  Show source$h=\frac{ b}{2~ a}$ 

The y coordinate of parabola vertex  Show source$k=\frac{ \Delta}{4~ a}$ 

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.
Tags and links to this website#
Tags:
quadratic_function · math_tables_quadratic_function · quadratic_function_formulas · quadratic_function_discriminant_formula · discriminant_formula · formula_for_quadratic_function_roots
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