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The equation provided is \( y = x^2 - 4x + 3 \), which is a quadratic equation. To find the vertex of this quadratic function, we can use the vertex formula for a quadratic equation in the form \( y = ax^2 + bx + c \), where the x-coordinate of the vertex is given by:

\[
x = \frac{-b}{2a}
\]

For the equation \( y = x^2 - 4x + 3 \), we have:
- \( a = 1 \)
- \( b = -4 \)

Substituting these values into the vertex formula:

\[
x = \frac{-(-4)}{2(1)} = \frac{4}{2} = 2
\]

Now that we have \( x = 2 \), we substitute this back into the equation to find the y-coordinate of the vertex:

\[
y = (2)^2 - 4(2) + 3 = 4 - 8 + 3 = -1
\]

Thus, the vertex of the quadratic function is \( (2, -1) \).

The correct answer is **D. (2, -1)**.

Would you like a detailed explanation of how this process works or have any questions?

Here are 5 related questions to expand your understanding:
1. How do you complete the square to find the vertex of a quadratic equation?
2. What are the effects of changing the value of \( a \) in a quadratic equation?
3. How can you identify the axis of symmetry from a quadratic equation?
4. What is the discriminant, and how does it relate to the vertex and roots of a quadratic?
5. How do you find the focus and directrix of a quadratic function?

**Tip:** The vertex form of a quadratic equation, \( y = a(x-h)^2 + k \), makes identifying the vertex \((h, k)\) much easier than the standard form.

What is the vertex of the graph of the function y = x^2 - 4x + 3?

Discover how to find the vertex of the quadratic function y = x^2 - 4x + 3 using the vertex formula. This guide provides a step-by-step solution, covering key algebraic concepts and graphing techniques. Ideal for high school students in Grades 9-10.

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