Certainly! Let's analyze each given function step-by-step to determine whether it is a quadratic function. A quadratic function is a polynomial of degree 2, meaning the highest power of [tex]\( x \)[/tex] in the function should be [tex]\( 2 \)[/tex].
1. Function: [tex]\( f(x) = 2x^3 + 2x^2 - 4 \)[/tex]
- The highest power of [tex]\( x \)[/tex] here is [tex]\( 3 \)[/tex] (the [tex]\( x^3 \)[/tex] term).
- Thus, this function is not quadratic.
2. Function: [tex]\( f(x) = -7x^2 - x + 2 \)[/tex]
- The highest power of [tex]\( x \)[/tex] here is [tex]\( 2 \)[/tex] (the [tex]\( x^2 \)[/tex] term).
- Thus, this function is quadratic.
3. Function: [tex]\( f(x) = -3x + 2 \)[/tex]
- The highest power of [tex]\( x \)[/tex] here is [tex]\( 1 \)[/tex] (the [tex]\( x \)[/tex] term).
- Thus, this function is not quadratic.
4. Function: [tex]\( f(x) = 0x^2 + 3x - 3 \)[/tex]
- While there is a quadratic term ([tex]\( 0x^2 \)[/tex]), its coefficient is [tex]\( 0 \)[/tex], effectively making it disappear.
- The highest power of [tex]\( x \)[/tex] in the remaining terms is [tex]\( 1 \)[/tex] (the [tex]\( x \)[/tex] term).
- Thus, this function is not quadratic.
After evaluating each function, we find that the only quadratic function is:
[tex]\[ f(x) = -7x^2 - x + 2 \][/tex]
This corresponds to the second function.
Therefore, the function that represents a quadratic function is:
[tex]\[ f(x) = -7x^2 - x + 2 \][/tex]
