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Quadratic Equation Solver

Standard Form: ax² + bx + c = 0

Calculation Results

Discriminant (Δ):
Root 1 (x₁):
Root 2 (x₂):
Vertex (x, y):

How to Use the Quadratic Solver

This tool functions like the polynomial solver on a Texas Instrument graphing calculator. To find the roots (x-intercepts) of a parabola, you must identify the coefficients of the quadratic equation in the standard form:

ax² + bx + c = 0

Simply enter the numerical values for a, b, and c into the input fields above and click "Calculate Roots". The tool will instantly compute the discriminant and the values of x.

Understanding the Discriminant

The discriminant (Δ = b² – 4ac) tells you how many solutions the equation has without solving the entire formula:

  • Δ > 0: There are two distinct real roots. The graph crosses the x-axis twice.
  • Δ = 0: There is exactly one real root. The graph touches the x-axis at its vertex.
  • Δ < 0: There are no real roots (only complex numbers). The graph does not touch the x-axis.

Why Use a Graphing Calculator for Algebra?

While manual calculation using the quadratic formula is essential for learning, Texas Instrument graphing calculators (like the TI-84 Plus) allow students and professionals to verify answers quickly. This online solver replicates that functionality, helping you check your homework or visualize the behavior of quadratic functions instantly.

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