Quadratic equation calculator

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
solve + factor + plot
show help ↓↓ examples ↓↓
Solve equation Write equation in factored form
Find area under/above x-axis Draw graph
example 1:ex 1:
Solve quadratic equation : $\frac{x^2}{4} - x + 1 = 0$.
example 2:ex 2:
Write equation $2 x^2 - 5x - 3 = 0$ in factored form.
example 3:ex 3:
Graph quadratic function $f(x) = \frac{x^2}{2} - 2x - \frac{5}{2}$.
example 4:ex 4:
Find area above x-axis if $f(x) = -\frac{3}{2} x^2 + 2x + 2$.

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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