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Calculators :: Quadratic equations and functions :: Quadratic Equations

This online calculator solves quadratic equation, finds factored form of a quadratic trinomial, finds area between the graph and x-axis and draws the graph of quadratic function. The calculator will generate a step-by-step explanation for each computation.

Quadratic equation calculator

Enter quadratic equation of the form ( ax2 + bx + c = 0 )
You can enter either integers (10), decimal numbers(10.12) or FRACTIONS (10/3). Important: The form will NOT let you enter wrong characters (like *, (, ), x, p,...) How to input?? 

Solve equation Write equation in factored form
Find area under/above x-axis Draw graph

About this calculator

This calculator can be used to: solve quadratic equation, factor quadratic trinomial, find area between the graph and x-axis, plot quadratic function.

About solving equation

To solve equation $ax^2 + bx + c = 0$ , this calculator uses formula:

$$x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}.$$

See this solver for step by step explanation.

About finding factored form

To factor trinomial $ax^2 + bx + c$ , this calculator uses formula

$$ax^2 + bx + c = a(x - x_1)(x - x_2)$$

Where $x_1$ and $x_2$ are solutions of the quadratic equation. If $x_1$ and $x_2$ don't exist that trinomial cannot be factored

About finding area

To area between the graph and x-axis this calculator uses formula

$$A = a(x_1^3-x_2^3) + b(x_1^2-x_2^2) + c(x_1-x_2)$$

Where $x_1$ and $x_2$ are solutions of the quadratic equation. $ax^2 + bx + c = 0$. If $x_1$ and $x_2$ don't exist than area doesn't exist too. If $x_1 = x_2$ than $area = 0$.

About graphing

See this calculator for step - by - step graphing.

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