Which equation represents a quadratic function?

Which equation represents a quadratic function?

• A. y = k/x
• B. y = x + b
• C. y = x^2
• D. y = ax + b

Answer: (C)

A quadratic function is defined by an equation of the form \(y = ax^2 + bx + c\), where \(a\), \(b\), and \(c\) are constants and \(a\) is not equal to zero. The key characteristic of a quadratic function is the presence of the \(x^2\) term, which gives the graph of the function a parabolic shape. The equation \(y = x^2\) fits this definition perfectly. In this case, \(a = 1\), \(b = 0\), and \(c = 0\). The function consists of only the \(x^2\) term, making it a quadratic with its vertex at the origin (0,0). The other equations do not have the necessary \(x^2\) term to be classified as quadratic functions. For example, the equation \(y = k/x\) represents a rational function, while \(y = x + b\) and \(y = ax + b\) are linear functions due to their first-degree terms. Thus, they do not exhibit the parabolic characteristics of quadratic functions.

A quadratic function is defined by an equation of the form (y = ax^2 + bx + c), where (a), (b), and (c) are constants and (a) is not equal to zero. The key characteristic of a quadratic function is the presence of the (x^2) term, which gives the graph of the function a parabolic shape.

The equation (y = x^2) fits this definition perfectly. In this case, (a = 1), (b = 0), and (c = 0). The function consists of only the (x^2) term, making it a quadratic with its vertex at the origin (0,0).

The other equations do not have the necessary (x^2) term to be classified as quadratic functions. For example, the equation (y = k/x) represents a rational function, while (y = x + b) and (y = ax + b) are linear functions due to their first-degree terms. Thus, they do not exhibit the parabolic characteristics of quadratic functions.