Which of the following functions is classified as a quadratic function?

Which of the following functions is classified as a quadratic function?

• A. y = mx + b
• B. y = ax^2 + bx + c
• C. f(x) = p(x) / q(x)
• D. y = 1

Answer: (B)

A quadratic function is defined as a polynomial function of degree two, which means it can be expressed in the form \( ax^2 + bx + c \), where \( a \), \( b \), and \( c \) are constants, and \( a \) is not equal to zero. The \( ax^2 \) term is the distinguishing characteristic that defines it as quadratic, as it indicates the function graph will produce a parabola when plotted. In comparison, the other options represent different types of functions. The first option is a linear function, characterized by a consistent slope and a constant \( b \) as the y-intercept. The third option depicts a rational function, which involves division of two functions and does not specifically represent quadratic behavior. The last option represents a constant function, which gives the same value (1 in this case) regardless of the input, not fitting the criteria for a quadratic function. Thus, the only function that fits the specific definition of a quadratic function is the one given in the correct answer, reinforcing the characteristics that all quadratic functions share.

A quadratic function is defined as a polynomial function of degree two, which means it can be expressed in the form ( ax^2 + bx + c ), where ( a ), ( b ), and ( c ) are constants, and ( a ) is not equal to zero. The ( ax^2 ) term is the distinguishing characteristic that defines it as quadratic, as it indicates the function graph will produce a parabola when plotted.

In comparison, the other options represent different types of functions. The first option is a linear function, characterized by a consistent slope and a constant ( b ) as the y-intercept. The third option depicts a rational function, which involves division of two functions and does not specifically represent quadratic behavior. The last option represents a constant function, which gives the same value (1 in this case) regardless of the input, not fitting the criteria for a quadratic function.

Thus, the only function that fits the specific definition of a quadratic function is the one given in the correct answer, reinforcing the characteristics that all quadratic functions share.