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Quadratic Equation Solver

Standard Form: ax² + bx + c = 0

Discriminant (Δ):
Root 1 (x₁):
Root 2 (x₂):
Vertex (h, k):

How to Use the Quadratic Solver

This tool mimics the functionality found on advanced graphing calculators like the Numworks. To solve a quadratic equation, simply identify the coefficients a, b, and c from the standard form equation ax² + bx + c = 0.

For example, in the equation 2x² – 4x + 2 = 0, you would enter:

  • a = 2
  • b = -4
  • c = 2

Click "Solve Equation" to find the roots (x-intercepts) and the vertex of the parabola.

Understanding the Discriminant

The discriminant (Δ = b² – 4ac) determines the nature of the roots without solving the entire equation:

  • Δ > 0: Two distinct real roots. The graph crosses the x-axis twice.
  • Δ = 0: One real root (repeated). The graph touches the x-axis at the vertex.
  • Δ < 0: Two complex roots. The graph does not touch the x-axis.

Why Use a Numworks Graphing Calculator?

The Numworks graphing calculator is renowned for its open-source approach and sleek design. It allows students to visualize mathematical concepts dynamically. While physical calculators are powerful, online tools like this one provide immediate access to these essential algorithms for homework and test preparation.

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