To classify and identify the terms of the function [tex]\( f(x) = 6x^2 + x - 12 \)[/tex], let's analyze its structure step by step.
First, we need to determine the type of function. A function is:
- Linear if it can be written in the form [tex]\( f(x) = ax + b \)[/tex], where [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are constants.
- Quadratic if it can be written in the form [tex]\( f(x) = ax^2 + bx + c \)[/tex], where [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex] are constants, and [tex]\( a \neq 0 \)[/tex].
Given the function [tex]\( f(x) = 6x^2 + x - 12 \)[/tex]:
1. The highest degree term is [tex]\( 6x^2 \)[/tex], which indicates that the function is quadratic since the highest power of [tex]\( x \)[/tex] is 2.
Next, let’s identify the terms within the function:
- Quadratic term: This is the term with [tex]\( x^2 \)[/tex]. In this function, it is [tex]\( 6x^2 \)[/tex].
- Linear term: This is the term with [tex]\( x \)[/tex]. In this function, it is [tex]\( x \)[/tex].
- Constant term: This is the term without [tex]\( x \)[/tex]. In this function, it is [tex]\( -12 \)[/tex].
Therefore, we can classify and identify the terms as follows:
- Quadratic function
- Quadratic term: [tex]\( 6x^2 \)[/tex]
- Linear term: [tex]\( x \)[/tex]
- Constant term: [tex]\( -12 \)[/tex]
So, the correct classification and identification are:
Quadratic function; quadratic term: [tex]\( 6x^2 \)[/tex]; linear term: [tex]\( x \)[/tex]; constant term: [tex]\( -12 \)[/tex].
Thus, the correct option is:
- Quadratic function; quadratic term: [tex]\( 6x^2 \)[/tex]; linear term: [tex]\( x \)[/tex]; constant term: -12
