onsider the following relation.

−3x^2−6x=−3x+2y−3x2−6x=−3x+2y

Step 2 of 3 :  

Evaluate the function found in the previous step at x=−2x=−2.

It seems the relation you provided has been repeated, and we need to clarify a bit. It looks like the original relation is:

\[
-3x^2 - 6x = -3x + 2y
\]

### Step 1: Solve for \( y \) in terms of \( x \)

1. Start by simplifying and isolating \( y \):
   \[
   -3x^2 - 6x = -3x + 2y
   \]

2. Add \( 3x \) to both sides to remove it from the right:
   \[
   -3x^2 - 3x = 2y
   \]

3. Now, divide both sides by \( 2 \) to isolate \( y \):
   \[
   y = \frac{-3x^2 - 3x}{2}
   \]
   \[
   y = -\frac{3}{2}x^2 - \frac{3}{2}x
   \]

### Step 2: Substitute \( x = -2 \) and evaluate \( y \)

Now that we have \( y \) as a function of \( x \):
\[
y = -\frac{3}{2}x^2 - \frac{3}{2}x
\]

Substitute \( x = -2 \):
\[
y = -\frac{3}{2}(-2)^2 - \frac{3}{2}(-2)
\]

Calculate each term:
1. \( (-2)^2 = 4 \)
2. \( -\frac{3}{2} \cdot 4 = -6 \)
3. \( -\frac{3}{2} \cdot (-2) = 3 \)

So,
\[
y = -6 + 3 = -3
\]

### Final Answer
When \( x = -2 \), \( y = -3 \).

---

Would you like further details or have any other questions?

Here are some related questions that might help you understand this process further:

1. How do we handle exponents when substituting values?
2. What are the steps for isolating a variable in an equation?
3. Why do we simplify terms before substituting a value?
4. How does dividing both sides of an equation affect each term?
5. Why is it important to evaluate each step individually when substituting?

**Tip:** Always simplify the equation fully before substituting values to minimize errors in calculation.

Consider the following relation.

−3x^2−6x=−3x+2y

Step 2 of 3: Evaluate the function found in the previous step at x = −2.

Learn how to evaluate a quadratic function -3x^2 - 6x = -3x + 2y at x = -2, using algebraic manipulation and substitution techniques. This guide is designed for high school students in Grades 9-11, covering the simplification and substitution of quadratic expressions.

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