Equation Solver: frequently asked questions
Straight answers to the questions people ask most about quadratic equations and the solver.
What is the quadratic formula?
For an equation ax² + bx + c = 0, the roots are given by x = (−b ± √(b² − 4ac)) / 2a. The Equation Solver applies this formula for you.
How does the discriminant decide the roots?
The discriminant is b² − 4ac. If it's positive, there are two distinct real roots; if zero, one repeated root; and if negative, no real roots exist.
How do I find the vertex?
The vertex's x-coordinate is x = −b / 2a. Plug that x into the equation to get the y-coordinate. The axis of symmetry is the vertical line through the vertex.
What does the parabola chart show?
The chart plots the curve so you can see its shape, direction (up if a > 0, down if a < 0), where it crosses the x-axis, and where its vertex lies.
Verdict
For roots, vertex, axis, and a visual chart of any quadratic, the Equation Solver gives you a complete answer instantly.