{"uid":"cap_l0RiHMwNf7kkqJNSikZ31","slug":"quadratic-equation-solver-0a6d0861","name":"Quadratic Equation Solver","description":"Solve ax^2 + bx + c = 0: real or complex roots, discriminant, vertex, axis of symmetry and factored form.","url":"https://math-geometry.x402tookit.com/quadratic-solve?utm_source=zero.xyz","method":"GET","headers":{},"bodySchema":{"type":"object","$schema":"https://json-schema.org/draft/2020-12/schema","required":["input"],"properties":{"input":{"type":"object","required":["type","method"],"properties":{"type":{"type":"string","const":"http"},"method":{"enum":["GET"],"type":"string"},"queryParams":{"type":"object","required":["a","b","c"],"properties":{"a":{"type":"number","description":"Coefficient of x^2 (not 0)"},"b":{"type":"number","description":"Coefficient of x"},"c":{"type":"number","description":"Constant term"}}}},"additionalProperties":false},"output":{"type":"object","required":["type"],"properties":{"type":{"type":"string"},"example":{"type":"object","properties":{"a":{"type":["null","number"]},"b":{"type":["null","number"]},"c":{"type":["null","number"]},"asOf":{"type":["null","string"]},"roots":{"type":["array","null"],"items":{"type":"number"}},"source":{"type":["null","string"]},"vertex":{"type":["null","object"],"properties":{"x":{"type":["null","number"]},"y":{"type":["null","number"]}}},"reasons":{"type":["array","null"],"items":{"type":"string"}},"summary":{"type":["null","string"]},"verdict":{"type":["null","string"]},"degraded":{"type":["boolean","null"]},"factored":{"type":["null","string"]},"rootType":{"type":["null","string"]},"disclaimer":{"type":["null","string"]},"notChecked":{"type":["array","null"],"items":{"type":"string"}},"sumOfRoots":{"type":["null","number"]},"yIntercept":{"type":["null","number"]},"opensUpward":{"type":["boolean","null"]},"discriminant":{"type":["null","number"]},"axisOfSymmetry":{"type":["null","string"]},"productOfRoots":{"type":["null","number"]}}}}}}},"responseSchema":null,"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.02","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"probe","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.02/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.02","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.02","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_OrjRCzIUCGAhWU1BT9pbU","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.02","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Solves ax² + bx + c = 0 and returns real or complex roots, discriminant, vertex, axis of symmetry, factored form, and other properties.","exampleAgentPrompt":"Can you solve the quadratic equation 2x² - 4x - 6 = 0? I need the roots, discriminant, vertex, axis of symmetry, and factored form.","exampleUseCases":[{"title":"Checking student homework answers","prompt":"My student wrote that the roots of x² - 5x + 6 = 0 are x=2 and x=3. Can you solve it properly and show me the discriminant, factored form, and vertex so I can verify their work?"},{"title":"Finding parabola vertex for graphing","prompt":"I need to graph the parabola 3x² + 12x + 9 = 0 — can you find the vertex, axis of symmetry, and whether it opens upward or downward?"},{"title":"Engineering equation with complex roots","prompt":"Solve the quadratic equation x² + 2x + 5 = 0 for me — I'm expecting complex roots, so show me all the details including the discriminant and factored form."}],"resultDescription":"Returns the three original coefficients (a, b, c), the discriminant value, root type (real/complex/repeated), the roots array, vertex coordinates (x, y), axis of symmetry equation, factored form string, sum and product of roots, y-intercept, whether the parabola opens upward, a human-readable summary, and optional degraded/disclaimer flags.","failureModes":["Coefficient a = 0 makes it not a quadratic — request likely rejected or undefined behavior","Non-numeric or missing a, b, or c parameters return an error","Very large or very small coefficients may cause floating-point precision issues in roots"],"whenToPreferThis":"Choose this endpoint when you need a full algebraic analysis of a single quadratic (degree-2 polynomial) including roots, vertex, discriminant, and factored form in one call. Prefer the cubic solver sibling for degree-3 polynomials or the linear system solver for multi-variable linear equations.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-11-03T18:36:59.549Z","isFirstParty":false,"canonicalSlug":"quadratic-equation-solver-0a6d0861"}