To find \( f(0) \), we substitute \( x = 0 \) into the expression for \( f(x) \):

The expression for \( f(x) \) is:

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

### Step 1: Substitute \( x = 0 \) into the equation:

\[
f(0) = (0)^2 + 2(0) - 2e^0 - 2
\]

### Step 2: Simplify:

\[
f(0) = 0 + 0 - 2(1) - 2
\]
\[
f(0) = -2 - 2 = -4
\]

So, \( f(0) = -4 \).

Would you like further details or have any other questions?

Here are 5 related questions for exploration:
1. What is the value of \( f(1) \)?
2. What is the value of \( f(-1) \)?
3. What is the value of \( f(2) \)?
4. What is the behavior of \( f(x) \) near \( x = 0 \)?
5. What is the tangent line to \( f(x) \) at \( x = 0 \)?

**Tip:** Evaluating functions at specific points helps in understanding the function's behavior and graph.

Learn how to find f(0) for the function f(x) = x^2 + 2x - 2e^x - 2 using step-by-step evaluation. This problem involves substituting x = 0 into the function equation and simplifying to find the value of f(0). Suitable for students in Grades 10-12 studying function evaluation and substitution.

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