Consider the following relation.

−x^2+2x−4y=−2y−x2+2x−4y=−2y

Step 1 of 3 :  

Rewrite the relation as a function of x.

To rewrite the relation as a function of \( x \), let's start by simplifying and isolating terms.

Given:
\[
-x^2 + 2x - 4y = -2y
\]

1. Move \( -2y \) to the left side to combine all \( y \)-terms:
   \[
   -x^2 + 2x - 4y + 2y = 0
   \]

2. Simplify:
   \[
   -x^2 + 2x - 2y = 0
   \]

3. Move the \( x \)-terms to the other side of the equation to isolate \( y \)-terms:
   \[
   -2y = x^2 - 2x
   \]

4. Divide both sides by \( -2 \) to solve for \( y \) in terms of \( x \):
   \[
   y = -\frac{x^2 - 2x}{2}
   \]

5. Simplify the right side:
   \[
   y = -\frac{1}{2}x^2 + x
   \]

So, the relation rewritten as a function of \( x \) is:
\[
y = -\frac{1}{2}x^2 + x
\]

Would you like to proceed with further steps or additional clarification?

### Questions for Further Practice:
1. Rewrite \( y = -\frac{1}{2}x^2 + x \) in terms of standard function notation, such as \( f(x) \).
2. Find the vertex of the function \( y = -\frac{1}{2}x^2 + x \).
3. Determine whether the function \( y = -\frac{1}{2}x^2 + x \) opens upwards or downwards.
4. Calculate the value of \( y \) when \( x = 2 \).
5. Solve \( y = -\frac{1}{2}x^2 + x \) for \( x \) when \( y = 0 \).

**Tip:** Remember that rewriting an equation as a function of \( x \) means isolating \( y \) so that it’s expressed entirely in terms of \( x \).

Consider the following relation.

−x^2+2x−4y=−2y

Step 1 of 3: Rewrite the relation as a function of x.

Explore how to rewrite the relation −x^2 + 2x − 4y = −2y as a function of x with step-by-step guidance. This example covers algebraic manipulation, isolating variables, and properties of quadratic functions. Ideal for students in Grades 8-10.

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