Which is a quadratic function? $$ \begin{array}{l}f(x)=2 x+x+3 \ f(x)=0 x^{2}-4 x+7 \ f(x)=5 x^{2}-4 x+5 \ f(x)=3 x^{3}+2 x+2\end{array} $$

Question

UpStudy AI · Accepted Answer

A **quadratic function** is a polynomial of degree 2, generally in the form:

$$ f(x) = ax^{2} + bx + c $$

where $$ a \neq 0 $$.

Let's analyze each of the given functions:

1. **$$ f(x) = 2x + x + 3 $$**
   $$
   f(x) = 3x + 3
   $$
   - **Degree:** 1 (Linear function)

2. **$$ f(x) = 0x^{2} - 4x + 7 $$**
   $$
   f(x) = -4x + 7
   $$
   - **Degree:** 1 (Linear function)

3. **$$ f(x) = 5x^{2} - 4x + 5 $$**
   - **Degree:** 2 (Quadratic function)

4. **$$ f(x) = 3x^{3} + 2x + 2 $$**
   - **Degree:** 3 (Cubic function)

**Conclusion:**

The quadratic function among the listed options is:

$$
f(x) = 5x^{2} - 4x + 5
$$
The quadratic function is $$ f(x) = 5x^{2} - 4x + 5 $$.

Which is a quadratic function? \( \begin{array}{l}f(x)=2 x+x+3 \\ f(x)=0 x^{2}-4 x+7 \\ f(x)=5 x^{2}-4 x+5 \\ f(x)=3 x^{3}+2 x+2\end{array} \)