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This online calculator is currently under heavy development. It may or it may NOT work correctly.
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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$y=\frac{a \cdot x+b}{c \cdot x+d}$ 

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

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

Linear function in pointslope form  Show source$y=a\left(xx_0\right)+y_0$ 

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$x=\frac{y_0 \cdot \left(x_1x_0\right)}{y_1y_0}+x_0$ 

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

Quadratic function in factored form  Show source$y=a\left(xx_1\right) \cdot \left(xx_2\right)$ 

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

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

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

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$x=\frac{y_0 \cdot \left(x_1x_0\right)}{y_1y_0}+x_0$ 

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:
$y=a \cdot x^{2}+b \cdot x+c$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):
$\Delta=b^{2}4~a \cdot c$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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