Which function represents a quadratic equation?

Which function represents a quadratic equation?

• A. f(x) = x + 3
• B. f(x) = x^2 + 4x + 4
• C. f(x) = 2^x
• D. f(x) = 1/x

Answer: (B)

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

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