Quadratic Function Formula – How To Find The Vertex Of A Quadratic Function?

What is Quadratic Function?

In elementary algebra, the quadratic formula would be the solution for quadratic equation. There are two possible techniques for solving the quadratic equation instead you put values in quadratic equation directly. These techniques are factoring, completing the square or graphing etc. Out of all these, working with quadratic formula is always the most convenient option.

Quadratic Equation

The general form of quadratic equation could be given as –

\[\large ax^{2} + bx + c =0 \]

Here x is the unknown variable, while a, b, and c are constants that could not be equal to the zero.

Standard Quadratic function

This is easy to verify the quadratic formula by satisfying the quadratic equations and inserting the former values to the latter. Hence, the standard quadratic formula in mathematics is given as below –

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

Here, the solution given y the quadratic formula is called as roots of quadratic equation. Geometrically, roots are used to give values on the parabola where y crosses the x-axis. If there is some formula whose yield is calculated equal to zero then this is easy to find immediately how many real zeros a particular quadratic equation has.

Quadratic Equation Formula

The Greek mathematicians are using many geometrical methods to solve quadratic equations. There is one algebraic technique that is more popular than geometric techniques of Euclid. It mostly gives only one root as the output or sometimes both roots are also positive. One Indian mathematician defined this formula explicitly and it could be written as given below.

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

With these formulas, you can solve or find roots for almost any quadratic equation by plugging the values directly into formula.