Which of the following represents the standard form of a quadratic function?

The standard form of a quadratic function is represented as ( y = ax^2 + bx + c ). In this formula, ( a ), ( b ), and ( c ) are constants, with ( a \neq 0 ). The term ( ax^2 ) indicates that the function is quadratic because it involves ( x ) raised to the second power. The presence of the linear term ( bx ) and the constant term ( c ) completes the expression, allowing it to encompass all parabolas that open upwards or downwards depending on the sign of ( a ).

This form is essential in identifying the coefficients that influence the shape and position of the parabola on the Cartesian plane. Specifically, the value of ( a ) determines the direction and width of the parabola, while ( b ) influences the position of the vertex along the x-axis, and ( c ) establishes the function's y-intercept.

The other formats listed represent different forms of quadratic functions or even linear functions; for example, the first choice is a linear equation. Therefore, the recognition of the correct structure of a quadratic equation is crucial in identifying the standard form is what makes the given answer valid.