To solve this question, we need to evaluate $f(-2)$ for the function given by:

$f(x) = x^2 + 3x - 2$

Step 1: Substitute $x = -2$ into the function

Let's replace $x$ with $-2$ in the expression.

$f(-2) = (-2)^2 + 3(-2) - 2$

Step 2: Calculate each term

1. $(-2)^2 = 4$
2. $3(-2) = -6$
3. $-2$ (the constant term remains as is)

So, we have:

$f(-2) = 4 - 6 - 2$

Step 3: Simplify

Now, combine the terms:

$f(-2) = 4 - 6 - 2 = -4$

Final Answer

$f(-2) = -4$

Would you like a detailed breakdown of the steps or have any questions on this solution?

Here are five related questions for further exploration:

1. What would $f(2)$ be for the function $f(x) = x^2 + 3x - 2$?
2. How do you find the zeros of the function $f(x) = x^2 + 3x - 2$?
3. What is the derivative of $f(x) = x^2 + 3x - 2$ with respect to $x$?
4. How do you determine whether the function $f(x) = x^2 + 3x - 2$ has a maximum or minimum point?
5. What is the y-intercept of the function $f(x) = x^2 + 3x - 2$?

Tip: When substituting values into an expression, be careful with negative signs, especially when squaring negative numbers.