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The task is to identify whether each function listed is quadratic or not. A quadratic function is any function of the form \( f(x) = ax^2 + bx + c \), where \( a \neq 0 \).

Let's go through each function:

1. **\( f(x) = 3x^2 - 4x \)**  
   This is quadratic, as it follows the form \( ax^2 + bx \) with \( a = 3 \) and \( b = -4 \).  
   **Answer:** Yes.

2. **\( f(x) = \sqrt{3x - 2x^2} \)**  
   The square root complicates the form. Although there is an \( x^2 \) term inside the square root, the presence of the square root itself makes this not a quadratic function.  
   **Answer:** No.

3. **\( f(x) = x + 7 \)**  
   This is a linear function because it lacks an \( x^2 \) term.  
   **Answer:** No.

4. **\( f(x) = x^2 + 7x - 1 \)**  
   This follows the quadratic form \( ax^2 + bx + c \) with \( a = 1 \), \( b = 7 \), and \( c = -1 \).  
   **Answer:** Yes.

5. **\( f(x) = (x + 2)(x - 4) \)**  
   Expanding this gives \( f(x) = x^2 - 4x + 2x - 8 = x^2 - 2x - 8 \), which is quadratic.  
   **Answer:** Yes.

6. **\( f(x) = x^2 + 1 \)**  
   This is a standard quadratic function of the form \( ax^2 + bx + c \).  
   **Answer:** Yes.

7. **\( f(x) = x + 1 \)**  
   This is a linear function because it lacks an \( x^2 \) term.  
   **Answer:** No.

8. **\( f(x) = x(x + 2x^{1/2}) - 1 \)**  
   The presence of \( x^{1/2} \) (square root of \( x \)) means this function is not quadratic.  
   **Answer:** No.

9. **\( f(x) = 2x \)**  
   This is linear, as there is no \( x^2 \) term.  
   **Answer:** No.

10. **\( f(x) = 2x^2 - 4x \)**  
   This follows the quadratic form \( ax^2 + bx \), with \( a = 2 \) and \( b = -4 \).  
   **Answer:** Yes.

Let me know if you'd like further clarification on any of these, or if you have any questions!

### Relative Questions:
1. What defines a quadratic function compared to other types of functions?
2. How do you expand the expression \( (x + 2)(x - 4) \)?
3. Why is \( f(x) = \sqrt{3x - 2x^2} \) not considered a quadratic function?
4. Can a function be quadratic if it contains square roots?
5. What is the general form of a linear function?

### Tip:
When checking if a function is quadratic, always ensure that the highest power of \( x \) is exactly 2, and there are no square roots or higher powers of \( x \).

Identify whether each function is quadratic or not.

Learn to identify quadratic functions from a set of different equations, including expanding factored expressions and checking the general form ax^2 + bx + c. Suitable for Grades 8-10.

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