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Quadratic Solver

Algebra

Solve ax² + bx + c = 0; nature of roots; vertex; graph.

Coefficients

Equation: 1 x² + -3 x + 2 = 0

Results

Discriminant Δ = b² − 4ac1
Nature of rootstwo real distinct roots
Root 12
Root 21
Vertex (h, k)(1.5, -0.25)
Axis of symmetryx = 1.5
Y-intercept(0, 2)
X-intercepts(2, 0), (1, 0)

Plot of y = a x² + b x + c

vertex (1.5, -0.25)21

Frequently asked questions

▶What does the Quadratic Solver do?

The Quadratic Solver is an interactive algebra lab where you change inputs and the answers update live, helping you build intuition without doing the arithmetic by hand.

▶Who should use the Quadratic Solver?

Students from primary to senior secondary classes, parents helping with homework, and anyone revising algebra can use this lab to check answers and explore "what-if" scenarios.

▶Is the Quadratic Solver free to use?

Yes. Every lab on math.suparnpatra.com is free and runs entirely in your browser : nothing is sent to a server.

▶Does the Quadratic Solver work offline?

Once the page is loaded, all calculations run locally in JavaScript, so you can keep using it even on a flaky connection.

▶How accurate are the results?

Results use standard JavaScript double-precision arithmetic and the textbook formula for algebra. We never display scientific notation : numbers are shown as ordinary decimals you can read at a glance.