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Quadratic Formula Calculator

Algebraic tool for solving quadratic equations via the Quadratic Formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$. Analyzes root nature via discriminant $\Delta = b^2 - 4ac$ and computes the vertex $(h, k)$.

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Formula: Quadratic Formula: x = (-b ± √(b² - 4ac)) / (2a). Discriminant Δ = b² - 4ac. Vertex: h = -b / (2a), k = c - (b² / (4a)).

In-Depth Guide & Mathematical Methodology

📐 Discriminant & Root Classification

Δ > 0: Two distinct real roots. Parabola intersects x-axis twice.

Δ = 0: One repeated real root (x = -b / 2a). Parabola touches x-axis at vertex.

Δ < 0: Two complex conjugate roots (x = u ± vi). Parabola does not intersect x-axis.

Frequently Asked Questions (FAQ)

What is the Quadratic Formula Calculator and how does it work?

Algebraic tool for solving quadratic equations via the Quadratic Formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$. Analyzes root nature via discriminant $\Delta = b^2 - 4ac$ and computes the vertex $(h, k)$.

How do I use this Quadratic Formula Calculator?

Enter coefficient $a$ (non-zero). Enter coefficient $b$. Enter constant $c$. View discriminant $\Delta$, roots $x_1$ and $x_2$, and vertex coordinates.

What mathematical formula is used in this calculation?

Quadratic Formula: x = (-b ± √(b² - 4ac)) / (2a). Discriminant Δ = b² - 4ac. Vertex: h = -b / (2a), k = c - (b² / (4a)).

Is the Quadratic Formula Calculator on FindCalculator free to use?

Yes, all 330+ interactive tools on FindCalculator.online are 100% free, run directly in your browser without registration, and do not store your private calculation data.

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