Transform each quadratic function in the form y=ax²+ bc+c
1)y-x+5=(x-2)²

Let's transform the given quadratic equation \( y - x + 5 = (x - 2)^2 \) into the standard form \( y = ax^2 + bx + c \).

### Step 1: Expand the squared term
First, expand the right-hand side of the equation:
\[
(x - 2)^2 = (x - 2)(x - 2) = x^2 - 4x + 4
\]
Now, the equation becomes:
\[
y - x + 5 = x^2 - 4x + 4
\]

### Step 2: Simplify the equation
Next, move all terms that are not related to \( y \) to the right-hand side:
\[
y = x^2 - 4x + 4 + x - 5
\]

### Step 3: Combine like terms
Simplify the expression on the right-hand side:
\[
y = x^2 - 4x + x + 4 - 5
\]
\[
y = x^2 - 3x - 1
\]

### Final Answer:
The equation in the form \( y = ax^2 + bx + c \) is:
\[
y = x^2 - 3x - 1
\]

Do you need any details or have questions?

Here are 5 questions that could extend the understanding:
1. How do you expand binomials like \( (x-2)^2 \)?
2. What is the significance of combining like terms in this transformation?
3. Can you graph this quadratic function and interpret its key features (vertex, intercepts)?
4. How would completing the square apply to this equation?
5. What does the coefficient \( a = 1 \) tell you about the shape of the parabola?

**Tip**: Always check for like terms when simplifying quadratic equations to avoid errors.

Transform each quadratic function in the form y=ax²+ bx+c: 1) y - x + 5 = (x - 2)²

Learn how to transform the quadratic equation y - x + 5 = (x - 2)² into the standard form y = ax² + bx + c. This problem includes expanding binomials, simplifying expressions, and understanding the structure of quadratic functions. Suitable for students in Grades 8-10.

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