Discriminant
1
Math Utility
Quadratic Equation Solver
Solve quadratic equations in standard form and inspect the discriminant, roots, axis of symmetry, and vertex without working the formula by hand.
Axis of symmetry
1.5
Vertex x
1.5
Vertex y
-0.25
Frequently asked questions
What equation form does this solve?
It solves quadratic equations in the standard form ax² + bx + c = 0, where a must not be zero.
What does the discriminant show?
The discriminant b² - 4ac determines the root type: positive gives two real roots, zero gives one repeated real root, and negative gives complex roots.
What is the vertex?
The vertex is the turning point of the parabola. Its x-coordinate is -b / 2a, and the y-coordinate is found by substituting that x-value back into the quadratic.
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