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The uploaded image shows a mathematical problem involving the graphs of the functions \( f(x) = -2x + 4 \) and \( g(x) = ax^2 + bx + c \). Let's break down the problem:

### The Graphs
1. **\( f(x) = -2x + 4 \)** is a linear function with a slope of \(-2\) and a y-intercept at \( (0, 4) \).
2. **\( g(x) = ax^2 + bx + c \)** is a quadratic function, and its graph is a parabola. 

### Questions
**5.1 Determine the values of \( a \), \( b \), and \( c \) for \( g(x) \).**

- The exact values of \( a \), \( b \), and \( c \) would depend on the points provided by the graph or additional information, such as vertex or intercepts. Without specific numerical information from the graph or the context, we would need to analyze the shape and position of the parabola to deduce these values.

**5.2 Write down the coordinates of \( A \) and \( B \).**

- Points \( A \) and \( B \) are likely the points of intersection between the line \( f(x) = -2x + 4 \) and the parabola \( g(x) \). The exact coordinates would require solving the system of equations:
  \[
  -2x + 4 = ax^2 + bx + c
  \]
  Again, the solution requires the exact forms of \( a \), \( b \), and \( c \), which are not visible from the image alone.

**5.3 Determine the values of \( x \) for which \( f(x) \geq g(x) \).**

- This is solved by finding the intervals where the line \( f(x) \) lies above or on the parabola \( g(x) \). Mathematically, this would be where \( -2x + 4 \geq ax^2 + bx + c \). This inequality could be solved by finding the roots of the quadratic equation formed when setting \( -2x + 4 = ax^2 + bx + c \) equal and analyzing the intervals.

If you can provide any additional values or ask for specific mathematical steps, I can offer more precise answers!

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Here are some related questions:

1. How do you determine the vertex of the parabola \( g(x) = ax^2 + bx + c \)?
2. What is the significance of the intersection points \( A \) and \( B \) on the graph?
3. How would you solve the system of equations formed by \( f(x) = g(x) \) to find the points \( A \) and \( B \)?
4. How does the discriminant of the quadratic equation relate to the number of intersection points?
5. What does the inequality \( f(x) \geq g(x) \) represent graphically?
6. How would changing the value of \( a \) affect the shape and orientation of the parabola?
7. How can you determine the axis of symmetry for the parabola?
8. What is the method to determine whether the parabola opens upwards or downwards?

**Tip**: When comparing a linear function and a quadratic function, remember that the line can intersect the parabola at most twice, which gives either two, one, or no intersection points.

Explore the intersection of linear function f(x) = -2x + 4 and quadratic function g(x) = ax^2 + bx + c. Understand how to determine coefficients a, b, and c, find intersection points A and B, and analyze inequalities involving these functions. Suitable for high school students studying functions and inequalities in algebra.

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