The equation ax^2 + bx + c = 0 is a standard form of a quadratic equation, where a , b , and c are constants, and x represents the variable. The coefficient a must be non-zero for the equation to be quadratic. This type of equation graphs as a parabola, which can open either upwards or downwards depending on the sign of a . To find the values of x that satisfy the equation, one can use the quadratic formula, x = \frac-b \pm \sqrt{b^2 - 4ac}2a . The term b^2 - 4ac is known as the discriminant, which determines the nature of the roots: two real roots, one real root, or two complex roots.