Which statement defines a quadratic function?

• A. y = ax^2 + bx + c
• B. y = a^x + b
• C. y = sqrt(x)
• D. y = x^3 + 2

Answer: (A)

Quadratic functions come from polynomials where the highest power of x is 2, expressed as y = ax^2 + bx + c with a ≠ 0. That x^2 term makes the graph a parabola, which is the hallmark of a quadratic function. The other forms are not quadratic: an exponential function has the variable in the exponent (y = a^x + b), a square root function involves the square root of x (y = sqrt(x)), and a cubic function has the highest power x^3 (y = x^3 + 2). So the expression with the x^2 term is the one that defines a quadratic function.