Quadratic function calculator
Calculator helpful during common operations related to quadratic function such as calculating value at given point, calculating discriminant or finding out function roots.

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.
Feel free to send any ideas and comments !
⌛ Loading...

Some facts

  • The quadratic function is a function that can be prepresented in the form:
    y=a x2+b x+c y= a~{ x}^{2}+ b~ x+ c
    where:
    • yy - function value (the function value at single point x, often marked as f(x)),
    • xx - function argument (called also independent value),
    • aa, bb, cc - quadratic function coefficients (numbers just before x2, 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.
  • 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):
    Δ=b24 a c \Delta={ b}^{2}-4~ a~ c
    where:
    • Δ\Delta - dicriminant of the quadratic function,
    • aa, bb, cc - quadratic function coefficients (numbers just before x2, x and free parameter).
    then the following scenarios are possible:
    • 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=b2 a 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:
      x1=bΔ2 a x_1=\frac{- b-\sqrt{ \Delta}}{2~ a}
      x2=b+Δ2 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

What tags this calculator has

Permalink

Links to external sites (leaving Calculla?)

JavaScript failed !
So this is static version of this website.
This website works a lot better in JavaScript enabled browser.
Please enable JavaScript.