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- Quadratic equations 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.

example 1:

Solve quadratic equation : $\frac{x^2}{4} - x + 1 = 0$.

example 2:

Write equation $2 x^2 - 5x - 3 = 0$ in factored form.

example 3:

Graph equation $f(x) = \frac{x^2}{2} - 2x - \frac{5}{2}$.

example 4:

Find area above x-axis if $f(x) = -\frac{3}{2} x^2 + 2x + 2$.

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

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.

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

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 $area = 0$.

See this calculator for step - by - step graphing.

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