To determine which function represents a quadratic function, we first need to understand the definition of a quadratic function. A quadratic function is a polynomial of degree 2, meaning the highest power of \(x\) is \(x^2\).
Let's examine each of the given functions:
1. \( f(x) = 2x^3 + 2x^2 - 4 \)
- The highest power of \(x\) in this function is \(x^3\), which means it is a polynomial of degree 3. Therefore, it is not a quadratic function.
2. \( f(x) = -7x^2 - x + 2 \)
- The highest power of \(x\) in this function is \(x^2\), which means it is a polynomial of degree 2. Therefore, it is a quadratic function.
3. \( f(x) = -3x + 2 \)
- The highest power of \(x\) in this function is \(x\), which means it is a polynomial of degree 1. Therefore, it is not a quadratic function.
4. \( f(x) = 0x^2 + 3x - 3 \)
- Although this function contains an \(x^2\) term, it has a coefficient of 0, so the highest power of \(x\) that actually affects the function is \(x\). Therefore, it is effectively a polynomial of degree 1 and is not a quadratic function.
Summarizing our findings, the function that represents a quadratic function is:
[tex]\[ f(x) = -7x^2 - x + 2 \][/tex]
Thus, the function [tex]\( f(x) = -7x^2 - x + 2 \)[/tex] is the quadratic function among the given options.
