Quadratic Equations

Solve second-degree equations using the quadratic formula, completing the square, and factoring techniques.

Try the Solver

Understanding Quadratics

Learn how to solve quadratic equations using various methods and explore their graphical representations.

Standard Form

The general quadratic equation is: $ ax^2 + bx + c = 0 $
Where $ a $, $ b$, and $c$ are coefficients with $ a ≠ 0 $.

Quadratic Formula

Use the formula to find solutions: $ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} $

The discriminant $ b^2 - 4ac $ determines the nature of the roots:

  • Positive → Two real solutions
  • Zero → One real solution (repeated root)
  • Negative → Two complex solutions

Graph Visualization

Parabbolic shape with vertex at the curve's lowest/highest point.

Factoring

Break down the equation into binomial factors like: $ (x - p)(x - q) = 0 $

Completeting the Square

Rearrange the equation into perfect square form: $ (x + d)^2 = e $

Graphing

Find the vertex and intercepts to plot the characteristic parabola.

section id="quadratic-solver" class="container mx-auto px-4 md:px-6 py-16 bg-gradient-to-r from-blue-50 to-indigo-100 rounded-3xl shadow-xl mb-20">

Quadratic Equation Solver