Quadratic Formula Calculator - Calculatorall.com

Algebra is an important part of mathematics and within algebra an important concept is that of quadratic equation. This quadratic formula calculator also deals with the same to solve quadratic equations for you. Quadratic equation is actually a second degree polynomial equation in following form.

ax2 + bx + c = 0


where the value of x is not known, a is quadratic coefficient, b is linear coefficient, while c is the constant. All a, b, c are the numerals and are called as equation's coefficients. And they are all known numbers. Also, a cannot have 0 value otherwise this equation will become linear instead of quadratic. There are different options that you can try for solving quadratic equations including factoring, use of quadratic formula, graphing or completing squares. Here we'll only be discussing how quadratic formula is used, and basics of the completing square method as deriving the formula includes that as well. Given below is the formula itself and how it's derived.

Deriving Quadratic Formula - Calculatorall.Com

Deriving Quadratic Formula

Deriving Quadratic Formula - Calculatorall.Com

Here, we can complete square using below mentioned relationship:

x2 + bx + c = (x - h)2 + k

Moving forward with the derivation using the relationship:

Quadratic Formula Calculator - Calculatorall.com

The +- here exists as function of calculating square roots, making positive as well as negative roots of quadratic equation. Values of x that are found by the quadratic formula calculator using this above mentioned formula are quadratic equation's roots representing values of x where parabola crosses x-axis. Besides, quadratic formula can also be used for finding axis of parabola's symmetry. Also keep it in mind that there are quite a few real-world applications of quadratic formula like calculating areas, speed and trajectories of projectile, etc.

How It Works

This quadratic formula calculator also works on the principles of quadratic equation and can be used for solving such equations. All you have to do is to enter the values of a, b and c in the given spaces and click on calculate button. The result shows you two imaginary solutions and the positive and negative values of x.
So, regardless of where you want to apply the results, use this quadratic formula calculator for accurately solving quadratic equations.

Unit Conversion Helper


Other Calculators