Quadratic Formula Calculator – Guide & Formulas
Solve any quadratic equation using the quadratic formula. Calculates real and complex roots, vertex coordinates, and displays step-by-step discriminant steps.
Solve equations in the standard form ax² + bx + c = 0 instantly. Learn how the discriminant determines the number of solutions and whether they are real or complex.
Key Takeaway
Use the free Quadratic Formula Calculator to solve any quadratic equation using the quadratic formula. calculates real and complex roots, vertex coordinates, and displays step-by-step discriminant steps. Get instant results with step-by-step explanations.
How to Use the Quadratic Formula Calculator
- Enter the coefficient "a" (must not equal 0).
- Enter the coefficient "b" and the constant "c".
- Observe the calculated roots (real or imaginary/complex).
- Examine the step-by-step discriminant value and the coordinates of the parabola vertex.
The Formula
Variable Definitions
- a, b, c: Coefficients of the equation
- b^2 - 4ac: The discriminant (Δ) determining root properties
Solving x² - 5x + 6 = 0
A student needs to find the solutions to the equation where a = 1, b = -5, and c = 6.
- Step 1: Input parameters a = 1, b = -5, c = 6.
- Step 2: Calculate the discriminant: (-5)² - 4(1)(6) = 25 - 24 = 1.
- Step 3: Since the discriminant (1) is positive, there are 2 real roots.
- Step 4: Calculate roots: x = (5 ± √1) / 2 = 3 and 2.
Frequently Asked Questions
What does the discriminant (Δ) tell us?
If Δ > 0, there are two distinct real roots. If Δ = 0, there is exactly one repeating real root. If Δ < 0, there are two complex (imaginary) conjugate roots.
What is the vertex of a quadratic function?
The vertex is the minimum or maximum point of the parabola. The x-coordinate is found with -b/(2a), and the y-coordinate is the function value at that x.
Can coefficient "a" be zero?
No. If a = 0, the equation is linear (bx + c = 0) and cannot be solved using quadratic principles.