https://file.aiquickdraw.com/mathbot/file/1727378481828n60px7n4.jpg

Let's analyze the given functions and statements:

1. **Function A: \( g(x) = -\frac{3}{2}x + 4 \)**  
   This is a linear function. Linear functions do not have maxima or minima, since they extend infinitely in both directions.

2. **Function B: \( f(x) = (x + 2)(x + 6) \)**  
   Expanding this function:  
   \[
   f(x) = x^2 + 8x + 12
   \]  
   This is a quadratic function with a parabola opening upwards (since the coefficient of \( x^2 \) is positive). Therefore, it has a **minimum** point.

3. **Graph C:**  
   The graph in C is a parabola opening downwards, indicating that it has a **maximum** point.

Now, let's evaluate the statements:

1. **C has a maximum and A has a minimum.**  
   This is false because A (linear function) does not have a minimum.

2. **B has a minimum and C has a maximum.**  
   This is true because B (quadratic) has a minimum and C has a maximum.

3. **B and C have the same zeros.**  
   To check the zeros of B, we solve:  
   \[
   (x + 2)(x + 6) = 0 \implies x = -2, \, x = -6
   \]  
   For C, looking at the graph, the zeros seem different from B's. So, this statement is false.

4. **A and B have the same y-intercept.**  
   The y-intercept of \( g(x) \) is at \( (0, 4) \).  
   The y-intercept of \( f(x) \) is at \( (0, (0 + 2)(0 + 6)) = 12 \).  
   They are different, so this statement is false.

The correct statement is:  
**"B has a minimum and C has a maximum."**

Do you want a deeper explanation or have further questions?

### Related Questions:
1. How do you find the vertex of a quadratic function?
2. What is the general method to find the zeros of a polynomial?
3. How do you determine if a parabola opens upwards or downwards?
4. What are the characteristics of linear functions compared to quadratic functions?
5. How do you identify the y-intercept of a function graphically and algebraically?

**Tip:** Always check the direction of the parabola to determine if it has a maximum or minimum point.

Which statement is true about the functions A: g(x) = -3/2x + 4, B: f(x) = (x + 2)(x + 6), and the graph C?

Explore the differences between linear and quadratic functions by analyzing their graphs, maxima, minima, and zeros. This problem covers function analysis, suitable for students in Grades 9-12.

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