What does the Equation Solver do?
The Equation Solver solves quadratic equations of the form ax² + bx + c = 0. Enter the coefficients a, b, and c, and the tool returns the real roots, the vertex and axis of symmetry, and a chart of the parabola.
Common uses
- Find the roots — solve for the x-values where the parabola crosses the x-axis
- Locate the vertex — find the turning point (maximum or minimum) of the curve
- Identify the axis of symmetry — the vertical line that splits the parabola in half
- Visualize the curve — see the parabola chart to understand the shape and direction
Key features
- Real roots — computes the solutions using the quadratic formula when they exist
- Vertex & axis — reports the turning point and its vertical line of symmetry
- Parabola chart — plots the curve so you can see the behavior at a glance
How it works
The tool applies the quadratic formula: x = (−b ± √(b² − 4ac)) / 2a. The discriminant (b² − 4ac) determines the number of real roots: if it's positive there are two distinct roots, if zero there is one repeated root, and if negative there are no real roots. The vertex is at x = −b / 2a, and the axis of symmetry is that same vertical line.
Verdict
The Equation Solver gives you roots, vertex, axis, and a visual chart for any quadratic — everything you need to fully understand the equation. Open Equation Solver and solve it in seconds.