Which standard form represents a quadratic equation?

The correct representation of a quadratic equation is found in the format ax² + bx + c = 0. This form is known specifically as standard form for quadratic equations, where 'a', 'b', and 'c' are constants, and 'a' cannot be zero. Quadratic equations are characterized by their highest exponent being 2, which is represented by the x² term.

In this format, 'a' indicates the coefficient that affects the parabola's width and direction (whether it opens upwards or downwards), while 'b' and 'c' help determine the vertex and the position of the parabola on the coordinate plane. The overall structure is fundamental because it allows for various methods of solving the equation, such as factoring, using the quadratic formula, or completing the square.

The other options represent different types of equations: ax + b = c is a linear equation, which has a degree of 1; y = mx + b describes a linear function in slope-intercept form; and x² + 2x + 1 = 0, while similar in expression, is not presented in the standard form with explicit coefficients as per the convention (it can be rewritten to fit the format, but it’s not in