How to use it
- Write the equation as ax² + bx + c = 0 and enter a, b and c (use − for negative numbers).
- Read the discriminant b² − 4ac: it tells you whether there are two, one or no real solutions.
- Copy the roots in exact or decimal form, and check the vertex and the graph.
Questions and answers
What is the quadratic formula?
For ax² + bx + c = 0 with a ≠ 0, the solutions are x = (−b ± √(b² − 4ac)) / 2a. The part under the root, b² − 4ac, is called the discriminant.
What if the discriminant is negative?
Then there are no real solutions: the parabola never touches the x-axis. The equation still has two complex roots, written as p ± qi, which the calculator also shows.
My equation is not in the form ax² + bx + c = 0. What do I do?
Move every term to one side so the other side is 0, then combine like terms. For example, x² = 3x + 4 becomes x² − 3x − 4 = 0, so a = 1, b = −3 and c = −4.