It looks like you're asking for the process of completing the square for the quadratic expression \( y = x^2 - 4x + 3 \). Let's go through the steps.

### Step 1: Start with the given quadratic expression.
\[
y = x^2 - 4x + 3
\]

### Step 2: Isolate the constant term.
Move the constant term (+3) to the other side of the equation.
\[
y - 3 = x^2 - 4x
\]

### Step 3: Complete the square.
To complete the square, take half of the coefficient of the linear term (\(-4\)), square it, and add it to both sides. The coefficient of \(x\) is \(-4\), so:
\[
\left(\frac{-4}{2}\right)^2 = (-2)^2 = 4
\]
Add 4 to both sides of the equation:
\[
y - 3 + 4 = x^2 - 4x + 4
\]
\[
y + 1 = (x - 2)^2
\]

### Step 4: Simplify the equation.
Finally, solve for \(y\):
\[
y = (x - 2)^2 - 1
\]

### Result:
The quadratic expression \( y = x^2 - 4x + 3 \) can be rewritten by completing the square as:
\[
y = (x - 2)^2 - 1
\]

This form is useful for identifying the vertex of the parabola, which is at \((2, -1)\).

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Would you like more details on any of these steps or have any questions?

### Related Questions:
1. How does completing the square help in finding the vertex of a parabola?
2. Can the completing the square method be used for any quadratic equation?
3. What are other methods to solve quadratic equations besides completing the square?
4. How does the vertex form of a quadratic equation help in graphing it?
5. What is the significance of the discriminant in a quadratic equation?

### Tip:
When completing the square, always remember that the number added to complete the square is the square of half the coefficient of the linear term (the term with \(x\)).

Learn how to complete the square method for the quadratic equation y = x^2 - 4x + 3 with a detailed step-by-step solution. This problem covers key algebraic concepts, including the completing the square technique and its application to quadratic equations. Suitable for students in Grades 9-12.

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