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Classify the function as linear or quadratic and identify the quadratic, linear, and constant terms.

[tex]\( f(x) = 6x^2 + x - 12 \)[/tex]

A. Linear function; linear term: [tex]\( x \)[/tex]; constant term: [tex]\(-12\)[/tex]

B. Linear function; linear term: [tex]\( 6x^2 \)[/tex]; constant term: [tex]\(-12\)[/tex]

C. Quadratic function; quadratic term: [tex]\(-12x^2\)[/tex]; linear term: [tex]\(-6x\)[/tex]; constant term: [tex]\(-12\)[/tex]

D. Quadratic function; quadratic term: [tex]\( 6x^2 \)[/tex]; linear term: [tex]\( x \)[/tex]; constant term: [tex]\(-12\)[/tex]

Sagot :

GinnyAnswer
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
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