Mathematical Notebook Pro - Quadratic Equation Solver

Enter coefficients for equations of the form: ax² + bx + c = 0

Multiple approaches to solving quadratic equations with detailed steps

Current Equation

x²

+

x

+

= 0

Coefficient a

Coefficient of x² term (cannot be zero)

Coefficient b

Coefficient of x term (can be zero)

Coefficient c

Constant term (can be zero)

Solution Methods

Factor by grouping method • Universal solution method • Perfect square trinomial method

1

Factoring Method

Factor by grouping when possible

Ready

When factorable: ax² + bx + c = (px + q)(rx + s)

Solution Steps

Factored Form

2

Quadratic Formula

Universal solution method

Ready

The Quadratic Formula

x =

- b ± √

b² - 4ac

2a

Solution Steps

Formula Result

3

Completing the Square

Perfect square trinomial method

Ready

Completing the Square: ax² + bx + c = a(x + h)² + k

Solution Steps

Completed Square Form

Interactive Graph Visualization

Visualize your quadratic function with interactive controls

Zoom

Display

x: 0.00 y: 0.00

Graph Legend

Quadratic Function

Roots (x-intercepts)

Vertex (turning point)

Axis of Symmetry

Mathematical Analysis

Nature of Roots • Sum & Product Relations • Parabola Properties

Discriminant Analysis

Nature of roots determination

Δ = b² - 4ac

Solve an equation to see discriminant analysis

Root Properties

Vieta's formulas

Sum: -b/a

Product: c/a

Solve an equation to see root properties

Vertex Analysis

Parabola turning point

h = -b/2a

k = f(h)

Solve an equation to see vertex analysis

Comprehensive Results

Complete solution summary

📋

Solve an equation to see comprehensive results and analysis

Enter coefficients above and click "Solve Equation" to get started