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This online calculator is currently under heavy development. It may or it may NOT work correctly.
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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.
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quadratic_function · math_tables_quadratic_function · quadratic_function_formulas · quadratic_function_discriminant_formula · discriminant_formula · formula_for_quadratic_function_roots
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