Which equation can be classified as a quadratic equation?

A quadratic equation is defined as an equation of the form ( ax^2 + bx + c = 0 ) where ( a ), ( b ), and ( c ) are constants and ( a \neq 0 ). This format clearly represents a polynomial equation of degree 2, which is characterized by the highest exponent of the variable being 2. The presence of the ( x^2 ) term is essential; it signifies that the graph of the equation will be a parabola.

In contrast, the other options provided represent different types of equations. The equation of the form ( ax + b = 0 ) is linear, as it has the highest exponent of the variable ( x ) equal to 1. The equation ( y = mx + b ) is also linear, representing the slope-intercept form of a line, where ( m ) is the slope and ( b ) is the y-intercept. Lastly, ( xy + c = 0 ) signifies a relation in two variables that does not fit the standard form of polynomial equations, as it involves a product of the two variables, suggesting a type of relationship that is not quadratic.

Thus, the only equation that meets the