The problem asks us to evaluate the function $f(x) = 2x^2 + x + 2$ at $x = -2$. In other words, we need to find the value of $f(-2)$.

1. Problem Description

The problem asks us to evaluate the function $f(x) = 2x^2 + x + 2$ at $x = -2$. In other words, we need to find the value of $f(-2)$.

2. Solution Steps

To find $f(-2)$, we substitute $-2$ for $x$ in the expression for $f(x)$.

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

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

First, we calculate $(-2)^2$:

$$(-2)^2 = (-2) \times (-2) = 4$$

Then we substitute this value back into the equation:

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

Next, we multiply 2 by 4:

$$f(-2) = 8 - 2 + 2$$

Finally, we simplify:

$$f(-2) = 8$$

3. Final Answer

8