What is the general form of a quadratic function?

What is the general form of a quadratic function?

• A. y = ax + b
• B. y = ax^2 + c
• C. y = ax^3 + c
• D. y = a/c

Answer: (B)

The general form of a quadratic function is defined as \( y = ax^2 + bx + c \), where \( a \), \( b \), and \( c \) are constants, and \( a \) is not equal to zero. This form represents a parabola when graphed, and the key characteristic of a quadratic function is the presence of the \( x^2 \) term, which is the hallmark of its degree of 2. The option you've chosen, \( y = ax^2 + c \), simplifies this form by omitting the linear term \( bx \). While it's a specific case of a quadratic function (where \( b=0 \)), it still retains the essential feature of having \( x^2 \) included, which classifies it correctly as a quadratic function. The other choices do not meet the criteria for a quadratic function. The linear function \( y = ax + b \) only includes the first degree of \( x \) and therefore is not quadratic. The cubic function \( y = ax^3 + c \) incorporates \( x^3 \) and is classified as cubic, not quadratic. Lastly, \( y = a/c \) is merely a constant and does not involve

The general form of a quadratic function is defined as ( y = ax^2 + bx + c ), where ( a ), ( b ), and ( c ) are constants, and ( a ) is not equal to zero. This form represents a parabola when graphed, and the key characteristic of a quadratic function is the presence of the ( x^2 ) term, which is the hallmark of its degree of 2.

The option you've chosen, ( y = ax^2 + c ), simplifies this form by omitting the linear term ( bx ). While it's a specific case of a quadratic function (where ( b=0 )), it still retains the essential feature of having ( x^2 ) included, which classifies it correctly as a quadratic function.

The other choices do not meet the criteria for a quadratic function. The linear function ( y = ax + b ) only includes the first degree of ( x ) and therefore is not quadratic. The cubic function ( y = ax^3 + c ) incorporates ( x^3 ) and is classified as cubic, not quadratic. Lastly, ( y = a/c ) is merely a constant and does not involve