Quadratic Equation Solver
Standard Form: ax² + bx + c = 0
Discriminant (Δ):
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Root 1 (x₁):
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Root 2 (x₂):
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Vertex (h, k):
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How to Use the Quadratic Solver on TI-84 Plus CE
The Texas Instruments TI-84 Plus CE is a powerful tool for algebra students. While the calculator has a built-in "PolySmlt" app for solving polynomials, understanding the manual calculation process helps solidify the concepts of the Quadratic Formula.
Understanding the Discriminant
The discriminant is the part of the quadratic formula under the square root sign (b² – 4ac). It tells you how many real solutions the equation has:
- Positive Discriminant: Two distinct real roots.
- Zero Discriminant: Exactly one real root (the parabola touches the x-axis at one point).
- Negative Discriminant: No real roots (the solutions are complex numbers).
Finding the Vertex
On the TI-84 Plus CE, you can graph the equation to find the maximum or minimum point (the vertex). The x-coordinate of the vertex is found using x = -b / (2a). This calculator provides that coordinate instantly, saving you time during exams or homework.