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To determine the "opening" of the parabola given by the equation:

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

### Step-by-Step Breakdown:
1. **Standard Form**: The equation is in vertex form \(y = a(x - h)^2 + k\), where \(a = 2\), \(h = -3\), and \(k = -2\).
   
2. **Direction of Opening**: 
   - The value of \(a\) determines the direction of the parabola's opening. 
   - If \(a > 0\), the parabola opens **upward**.
   - If \(a < 0\), the parabola opens **downward**.
   
   In this case, \(a = 2\) (which is positive), so the parabola opens **upward**.

### Summary:
The parabola opens **upward**.

Would you like a deeper explanation of any part, or do you have any further questions?

Here are 5 related questions to expand on this:
1. How do you find the vertex of a parabola in vertex form?
2. What effect does changing the value of \(a\) have on the width of the parabola?
3. How would the graph change if \(a\) were negative?
4. How can you rewrite this equation in standard quadratic form?
5. How do you determine the axis of symmetry from a parabola in vertex form?

**Tip**: The larger the absolute value of \(a\), the narrower the parabola!

Determine the opening of the parabola y = 2(x + 3)^2 - 2.

Learn how to determine the direction of the opening of the parabola given by the equation y = 2(x + 3)^2 - 2. This problem covers the vertex form of a parabola and explains how the value of 'a' affects the direction of the opening. Suitable for students in Grades 9-11.

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