Give me best evaluating function and need sulution, table and graph

Here's the graph of the quadratic function \( f(x) = x^2 - 4x + 3 \). You can observe the minimum point at \( x = 2 \), where \( f(2) = -1 \). The table of values and graph illustrate how the function behaves over a range of \(x\) values.

### Table of Values:
| \( x \)  | \( f(x) = x^2 - 4x + 3 \) |
|---------|---------------------------|
| \( 0 \)  | \( f(0) = 3 \)            |
| \( 1 \)  | \( f(1) = 0 \)            |
| \( 2 \)  | \( f(2) = -1 \)           |
| \( 3 \)  | \( f(3) = 0 \)            |
| \( 4 \)  | \( f(4) = 3 \)            |

This function is a downward-facing parabola, with a minimum value at \( x = 2 \).

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### 5 Related Questions:
1. How do we determine the vertex of any quadratic function?
2. How does changing the coefficients in a quadratic function affect its shape?
3. What is the significance of the discriminant in a quadratic equation?
4. How can we apply this function to real-world optimization problems?
5. What happens when we shift or scale this quadratic function?

### Tip:
For any quadratic function \( ax^2 + bx + c \), the vertex occurs at \( x = -\frac{b}{2a} \), and this point gives either the maximum or minimum value of the function, depending on the sign of \(a\).

Explore how to evaluate and graph the quadratic function f(x) = x^2 - 4x + 3. This solution provides a detailed table of values, a graph, and explains key concepts such as the vertex and the shape of the parabola. Ideal for students in Grades 8-10.

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