Quadratic Equation Solver
Format: ax² + bx + c = 0
Discriminant (Δ):
Root 1 (x₁):
Root 2 (x₂):
Vertex (h, k):
Axis of Symmetry:
Graph Visualization
How to Solve Quadratics on the TI-84 Plus CE
The TI-84 Plus CE graphing calculator is a powerful tool for algebra students. While this online tool helps you find the roots and vertex instantly, understanding the steps on the physical device is essential for exams.
Understanding the Discriminant
The discriminant is the part of the quadratic formula under the square root: b² – 4ac. It tells you how many real solutions exist:
- If Δ > 0: There are two distinct real roots.
- If Δ = 0: There is exactly one real root (the parabola touches the x-axis).
- If Δ < 0: There are no real roots (the parabola does not touch the x-axis).
Finding the Vertex Manually
The vertex represents the minimum or maximum point of the parabola. You can find the x-coordinate (h) using the formula h = -b / (2a). Once you have h, substitute it back into the original equation to find k.