What is the quadratic formula?

The quadratic formula is x = (-b ± √(b²-4ac)) / 2a. It solves any quadratic equation ax²+bx+c=0 by calculating the discriminant Δ = b²-4ac and using it to find both roots.

What does the discriminant tell us?

The discriminant Δ = b²-4ac determines the nature of roots: (1) Δ > 0: two distinct real roots, (2) Δ = 0: one repeated real root, (3) Δ < 0: two complex conjugate roots.

How do I convert to vertex form?

Vertex form is y = a(x-h)²+k where (h,k) is the vertex. Calculate h = -b/2a and k = f(h). This form clearly shows the vertex coordinates and whether the parabola opens up (a>0) or down (a<0).

Can this solver handle complex roots?

Yes! When the discriminant is negative (b²-4ac < 0), the solver calculates complex roots in the form x = p ± qi where p is the real part and q is the imaginary part.

How do I use vertex form input?

Select 'Vertex Form' from the equation type dropdown. Enter a (leading coefficient), h (x-coordinate of vertex), and k (y-coordinate of vertex). The solver automatically converts a(x-h)²+k=0 to standard form and solves it.

What is factored form and when do I use it?

Factored form is a(x-r₁)(x-r₂)=0 where r₁ and r₂ are the roots. Use this when you already know the roots and want to find the standard form or verify solutions. Enter a (coefficient) and the two roots r₁ and r₂.

How do quadratic inequalities work?

Select 'Quadratic Inequality' and choose an operator (>, <, ≥, ≤). The solver finds the roots, creates a sign chart, and provides the solution in interval notation. For example, x²-5x+6 < 0 gives the solution x ∈ (2, 3).

Quadratic Equation Solver (ax² + bx + c = 0)

Solve quadratic equations with step-by-step solutions and parabola visualization.

Equation Input

Equation Form Choose the form of your equation

a (coefficient of x²) Must be non-zero

b (coefficient of x)

c (constant term)

x² + 5x + 6 = 0

Solution Methods

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Quadratic Equation Solver (ax² + bx + c = 0)

Equation Input

Solution Methods

Parabola Visualization

Support This Free Tool

Quick Access

Quadratic Equation Solver (ax² + bx + c = 0)

Equation Input

Solution Methods

Parabola Visualization

Support This Free Tool

Quick Access

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