What are the basics of quadratic formula and function, how you can solve quadratic equations. A calculator for…
f(x)=y

$\lim_{x \to \infty} \exp(-x) = 0$

$f(n) = n^5 + 4n^2 + 2 |_{n=17} \,$

Quadratic function is a polynomial mathematical function of this type:

f(x) = ±ax2 ± bx ± c    , where  a is not equal to 0
These functions are polynomials of second degree, because the highest degree of x is 2. Quadratic functions are widely used in mathematics, because they can be used to find the solutions of various types of math problems. Its name comes from the word “quadratum” in Latin, which means square – second degree.

a, b, c are called coefficients of the quadratic function. a has to be different from 0 (zero), or the function will be of first degree and not a quadratic one.

If a quadratic function is equal to zero – ±ax2 ± bx ± c = 0, we have a quadratic equation.

Example of a graph of the quadratic function -2x^2+5x+3

The graph of every quadratic function is a parabola (pic 1). The type of the parabola depends on the quadratic coefficients – a, b, c

a – determines the direction of the parabola and its radius. Ia a>0, the direction is upward, if a<0 – the direction of the parabola is downward.

b – determines the position of the parabola, according to the y-axis

c – determines the position of the parabola, according to the x-axis

To further explore how the graph depends on the coefficients, you can use our quadratic function grapher. There you can draw quadratic charts, by just entering a,b and c. You can also use our quadratic equation calculator, where you can not only see the chart of the function, but also you can calculate more different information about it.

The maximum/minimum, or the global extrema of the parabola of any quadratic function is equal to -b / 2a . (look also at the formulas at the right side of the site).

If we have an equation like:, the following formulas apply to it: