Quadratic equation
![Figure 1. Plots of quadratic function y = ax2 + bx + c, varying each coefficient separately while the other coefficients are fixed (at values a = 1, b = 0, c = 0)](/Images/godic/202502/09/Quadratic_equation_coefficients4844.png")
![Figure 2. For the quadratic function y = x2 − x − 2, the points where the graph crosses the x-axis, x = −1 and x = 2, are the solutions of the quadratic equation x2 − x − 2 = 0.](/Images/godic/202502/09/Polynomialdeg2.svg4844.png")
![Figure 3. Discriminant signs](/Images/godic/202502/09/Quadratic_eq_discriminant.svg4844.png")
![](/Images/godic/202502/09/La_Jolla_Cove_cliff_diving_-_024844.jpg")
- For the case of more than one variable, see Conic section or Quadratic form.
In elementary algebra, a quadratic equation (from the Latin quadratus for "square") is any equation having the form
where x represents an unknown, and a, b, and c represent known numbers such that a is not equal to 0. If a = 0, then the equation is linear, not quadratic. The numbers a, b, and c are the coefficients of the equation, and may be distinguished by calling them, respectively, the quadratic coefficient, the linear coefficient and the constant or free term.