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Quadratic Function Formula

Quadratic function is also a second degree polynomial function.  The graph of a quadratic function is a parabola. The parabola open upwards if a graph is made for the quadratic formula.

The point at which the function attains maximum or minimum value is the vertex of the quadratic function. When we say second degree, then the variable is raised to the second power like $x^{2}$ .

The quadratic function is a polynomial function of the form:

\[\large x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}\]

Where,
a, b and c are the variables given in the equation.

This formula is used to solve any quadratic equation and get the values of the variable or the roots.

Solved example

Question: Solve $x^{2}-6x+8=0$

Solution

Given,
a= 1,
b = 6
c = 8

Using the formula: $x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}$

$\frac{-6\,\pm (6)^{2}4\times 1\times 8}{2\times 1}=-2$

The roots are: $x_{1}=-2$ and $x_{2}=-4$