High School Quadratic Equation Solver
Enter the coefficients for the standard form: ax² + bx + c = 0
Solution Results
Discriminant (Δ)
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Roots (x)
Vertex (h, k)
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Form Type
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Step-by-Step (Quadratic Formula)
Parabola Visualization
Understanding Quadratics
Welcome to this interactive Quadratic Equation Solver. A quadratic equation is a polynomial equation of degree 2, usually written in the standard form ax² + bx + c = 0, where a, b, and c are known numbers, and x is the unknown variable. The coefficient a cannot be zero, or else the equation becomes linear, not quadratic.
The Quadratic Formula
The most robust way to solve these equations is using the Quadratic Formula. It can handle any quadratic equation, whether the roots are whole numbers, fractions, decimals, or even complex numbers. The formula is:
The term inside the square root, b² – 4ac, is called the Discriminant. It tells you about the nature of the roots without actually solving the whole equation.
Why use a Quadratic Equation Solver?
Manually calculating roots can be tedious, especially with large numbers or decimals. This tool instantly calculates the Discriminant to determine if the roots are real or complex. It then applies the formula to find exact values. Additionally, it visualizes the function as a parabola. The points where the parabola crosses the X-axis represent the roots (solutions) of the equation.
Key Concepts Explained
- Vertex: The highest or lowest point of the parabola. If a is positive, the parabola opens up (minimum vertex). If a is negative, it opens down (maximum vertex).
- Axis of Symmetry: The vertical line that passes through the vertex, dividing the parabola into two mirror images.
- Roots/Zeros: The x-values where y = 0.
Using our Quadratic Equation Solver helps students visualize the connection between the algebraic formula and the geometric curve.
FAQ
If a=0, it’s not a quadratic equation anymore; it becomes a linear equation (bx + c = 0). The graph would be a straight line.
It means the parabola never touches the X-axis. The solutions are “complex” or “imaginary” numbers involving i (the square root of -1).
Yes, this tool is completely free and runs directly in your browser using JavaScript.
Absolutely. You can enter decimals for coefficients a, b, and c.