https://file.aiquickdraw.com/mathbot/file/1725813441647n3nbgwsq.jpg

The expression given in the image is:

\[
x^2 - 2x + 3
\]

To put this expression in canonical form (or standard form), we need to rewrite it in the vertex form, which is:

\[
a(x - h)^2 + k
\]

where \( (h, k) \) is the vertex of the parabola.

### Steps to Convert to Canonical Form:

1. **Complete the square** on the quadratic term:

   Given \( x^2 - 2x + 3 \), start by completing the square for the \( x^2 - 2x \) part.

2. Rewrite \( -2x \) as part of the square:

   \[
   x^2 - 2x = (x - 1)^2 - 1
   \]

   This step involves adding and subtracting 1 to complete the square.

3. Substitute back into the expression:

   \[
   x^2 - 2x + 3 = (x - 1)^2 - 1 + 3
   \]

4. Simplify:

   \[
   (x - 1)^2 + 2
   \]

### Final Canonical Form:

\[
(x - 1)^2 + 2
\]

This is the canonical form of the given expression.

Would you like further details or have any questions?

Here are some related questions:
1. How do you determine the vertex of a quadratic function?
2. What is the significance of completing the square in finding the canonical form?
3. How do you identify the axis of symmetry from the canonical form?
4. Can you graph the function using its canonical form?
5. What are the applications of the canonical form in solving equations?

**Tip:** Completing the square is a helpful technique for rewriting quadratic expressions and finding maximum or minimum values easily!

Learn how to convert the quadratic equation x^2 - 2x + 3 into its canonical form using the method of completing the square. This step-by-step guide is ideal for students in Grades 8-10, covering key algebraic concepts and theorems.

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