Solve any quadratic equation with detailed steps, get the roots, vertex, and see the graph. Our AI-powered tool makes algebra easy and educational.
ax² + bx + c = 0
Enter your equation coefficients to get:
Enter the coefficients of your quadratic equation in the standard form: ax² + bx + c = 0
Solving your equation...
ax² + bx + c = 0
Two real solutions
x₁:
1
x₂:
-1
Discriminant (Δ):
4
Vertex (h, k):
(0, -1)
Vertex:
(0, -1)
x-intercepts:
x = 1, x = -1
y-intercept:
y = -1
Our AI doesn't just give you the answers - it shows you every step of the solving process, making it perfect for learning and understanding.
Visualize your quadratic equation with our interactive graph. Adjust zoom and positioning to explore the parabola and understand its key features.
Our Gemini-powered AI explains concepts clearly and provides mathematical insights beyond just mechanical steps, helping you truly understand the solutions.
A quadratic equation is a second-degree polynomial equation in a single variable x, where a, b, and c are constants (with a ≠ 0): ax² + bx + c = 0. Quadratic equations can be solved using various methods including factoring, completing the square, using the quadratic formula, or graphing.
The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), where a, b, and c are the coefficients of the quadratic equation ax² + bx + c = 0. This formula gives the two solutions (roots) of any quadratic equation.
The discriminant is the expression inside the square root of the quadratic formula: b² - 4ac. It determines the nature of the roots:
The vertex of a parabola is the highest or lowest point on the graph. For a quadratic function in the form f(x) = ax² + bx + c, the x-coordinate of the vertex is given by x = -b/(2a), and the y-coordinate can be found by substituting this x-value into the original equation. If a > 0, the parabola opens upward and the vertex is the minimum point. If a < 0, the parabola opens downward and the vertex is the maximum point.
Yes, our quadratic equation solver can handle complex roots when the discriminant is negative. It will display the results in the form a + bi, where i is the imaginary unit (√-1). The graph will still be shown, even though the parabola doesn't cross the x-axis in these cases.
Input the coefficients a, b, and c for your quadratic equation in the standard form ax² + bx + c = 0. For example, for x² + 2x - 3 = 0, enter a=1, b=2, and c=-3.
Press the "Solve Equation" button and our AI will calculate the solutions, discriminant, vertex, and generate a detailed step-by-step solution and graph.
View the summary of results, including the roots, discriminant, and vertex. Switch between tabs to see the interactive graph and detailed step-by-step solution.
In the Graph tab, you can adjust the zoom level and center position to better visualize the parabola and its key features like intercepts and vertex.
Use the "Example" button to see how the solver works with a pre-filled equation. You can then modify the coefficients to explore different types of quadratic equations and their solutions.