What is the standard form of a quadratic function?

The standard form of a quadratic function is expressed as ( y = ax^2 + bx + c ), where ( a ), ( b ), and ( c ) are constants and ( a \neq 0 ). This format is important because it clearly identifies the quadratic term ( ax^2 ), which indicates the parabola's shape and direction (opening upwards if ( a > 0 ) and downwards if ( a < 0 )). The coefficients ( b ) and ( c ) represent the linear term and the constant term, respectively, which affect the function's position and intercepts on the graph.

In contrast, the other formats do not represent a quadratic function. The first choice, which is linear in nature (( y = ax + b )), lacks the ( x^2 ) component, making it a linear equation rather than a quadratic one. The third choice also suggests a linear relationship, as it lacks the ( x^2 ) term entirely. Lastly, the fourth choice presents another quadratic equation format but misses the coefficient (constant ( a )) for the ( x^2 ) term, which is essential for portraying the function's degree.

Therefore, the correct answer not