Which function represents a quadratic equation?

A function is classified as a quadratic equation when it can be expressed in the standard form ( f(x) = ax^2 + bx + c ), where ( a ), ( b ), and ( c ) are constants, and ( a \neq 0 ). This means that the highest degree of the variable ( x ) is 2, which results in a parabolic graph.

The function provided as the correct answer, ( f(x) = x^2 + 4x + 4 ), meets the criteria for a quadratic equation. It is in the standard form with the term ( x^2 ) indicating that it has a degree of 2. The coefficients for this function are ( a = 1 ), ( b = 4 ), and ( c = 4 ).

In comparison, the other functions do not satisfy the conditions for being quadratic:

• The first function, ( f(x) = x + 3 ), is linear because the highest power of ( x ) is 1.

• The third function, ( f(x) = 2^x ), is an exponential function, not polynomial, and is not quadratic because it involves exponentiation of a base