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The student made a mistake in computing \((x + 3)^2\) correctly. Let's break it down:

### Step-by-Step Correction:

1. **Original Function:**
   \[
   f(x) = 2(x + 3)^2 - 4
   \]

2. **Expand \((x + 3)^2\):**
   \[
   (x + 3)^2 = x^2 + 6x + 9
   \]
   The student incorrectly skipped expanding this properly, directly substituting \(x^2 + 6x + 9\).

3. **Distribute the 2:**
   \[
   f(x) = 2(x^2 + 6x + 9) - 4
   \]
   \[
   f(x) = 2x^2 + 12x + 18 - 4
   \]

4. **Simplify the expression:**
   \[
   f(x) = 2x^2 + 12x + 14
   \]

So, the correct standard form of the function is:
\[
f(x) = 2x^2 + 12x + 14
\]

### Correct Answer to the Dropdowns:
- **The student did not:** compute \((x + 3)^2\) correctly.
- **The function in standard form is:** \(f(x) = 2x^2 + 12x + 14\).

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Would you like more details on any step? Here are some related questions for further practice:

1. How do you expand a binomial square \((a + b)^2\)?
2. What are the steps to correctly distribute a number over a trinomial?
3. How do you determine if a quadratic function is in standard form?
4. What is the difference between standard form and vertex form of a quadratic function?
5. How do you identify errors in the distribution process in algebraic expressions?

**Tip:** Always expand and simplify expressions fully before moving on to subsequent steps to avoid errors like the one in this problem.

Describe and correct the error a student made when writing the quadratic function f(x) = 2(x + 3)^2 - 4 in standard form.

Learn how to identify and correct errors in the expansion of a quadratic function. This problem involves expanding and simplifying the expression f(x) = 2(x + 3)^2 - 4, common in algebraic studies. Suitable for students in Grades 8-10.

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