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The given quadratic function is:

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

### Step 1: Determine the Direction of the Parabola
The general form of a quadratic function is \( y = a(x-h)^2 + k \), where:
- \(a\) controls the direction and the "stretch" or "compression" of the graph.
- If \(a > 0\), the parabola opens **upward**.
- If \(a < 0\), the parabola opens **downward**.

In this case, \(a = 2\), which is positive. Therefore, the parabola opens **upward**.

### Step 2: Determine the Stretch or Compression
- If \(|a| > 1\), the parabola is **stretched taller** compared to the parent function \( y = x^2 \).
- If \(0 < |a| < 1\), the parabola is **compressed shorter**.

Since \(|a| = 2 > 1\), the parabola is **stretched taller** by a factor of 2.

### Conclusion:
The parabola opens upward and is stretched taller by a factor of 2.

The correct answer is:
- "The parabola opens upward and is stretched taller by a factor of 2."

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Would you like more details or have any questions? Here are some related questions:

1. How do you find the vertex of the quadratic function?
2. What effect does the value \(h\) have in the vertex form of a parabola?
3. How does shifting a parabola horizontally and vertically work?
4. Can a quadratic function have a negative \(a\) but still be stretched?
5. What is the parent quadratic function and how does it look?

**Tip:** In the vertex form \(f(x) = a(x-h)^2 + k\), the vertex is \((h, k)\).

Describe the graph of the quadratic function f(x) = 2(x+2)^2 - 1 by stating which way the parabola opens and whether it is stretched taller or compressed shorter when compared to the parent quadratic function.

Learn how to describe the graph of the quadratic function f(x) = 2(x+2)^2 - 1, focusing on the parabola's direction and how it is stretched compared to the parent function. Perfect for students in Grades 9-12 studying graph transformations and quadratic functions.

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