Quadratic Formula Calculator
Solve any quadratic equation of the form ax² + bx + c = 0 instantly. Get step-by-step solutions, visualize the graph, and understand the roots.
📝 Input Coefficients
📊 Solution & Graph
Enter coefficients and click "Calculate Solutions" to see results.
❓ Frequently Asked Questions
What is the quadratic formula?
The quadratic formula is used to solve quadratic equations of the form ax² + bx + c = 0. The formula is:
x = [-b ± √(b² - 4ac)] / (2a)
This formula gives the solutions (roots) of the quadratic equation.
What does the discriminant tell us?
The discriminant (D = b² - 4ac) determines the nature of the roots:
- D > 0: Two distinct real roots
- D = 0: One real root (repeated)
- D < 0: Two complex roots
Can I use this calculator for any quadratic equation?
Yes, our calculator works for all quadratic equations of the form ax² + bx + c = 0. Simply enter the coefficients a, b, and c, and the calculator will provide the solutions along with a graph of the function.
What do the graph points represent?
The graph visualizes the quadratic function f(x) = ax² + bx + c. The points where the curve crosses the x-axis represent the real roots of the equation. The vertex of the parabola shows the maximum or minimum point of the function.