To determine which of the given functions is quadratic, we need to identify the highest degree of [tex]\(x\)[/tex] in each function. A quadratic function is defined as a polynomial of degree 2.
1. First function:
[tex]\[
f(x) = 2x + x + 3
\][/tex]
Simplifying this, we have:
[tex]\[
f(x) = 3x + 3
\][/tex]
The highest degree of [tex]\(x\)[/tex] in this function is 1, so this is a linear function.
2. Second function:
[tex]\[
f(x) = 0x^2 - 4x + 7
\][/tex]
Simplifying this, we have:
[tex]\[
f(x) = -4x + 7
\][/tex]
The highest degree of [tex]\(x\)[/tex] in this function is also 1, so this is another linear function.
3. Third function:
[tex]\[
f(x) = 5x^2 - 4x + 5
\][/tex]
The highest degree of [tex]\(x\)[/tex] in this function is 2, so this is a quadratic function.
4. Fourth function:
[tex]\[
f(x) = 3x^3 + 2x + 2
\][/tex]
The highest degree of [tex]\(x\)[/tex] in this function is 3, so this is a cubic function.
By identifying the functions based on their degrees, we conclude that the third function [tex]\( f(x) = 5x^2 - 4x + 5 \)[/tex] is the quadratic function. Therefore, the correct answer is:
[tex]\[
\boxed{3}
\][/tex]
