To find $f(3)$ using the function rule given, we substitute $x = 3$ into the function $f(x) = 2x^2 + 4x + 12$.

Let's calculate:

$f(3) = 2(3)^2 + 4(3) + 12$

First, compute $3^2$:

$3^2 = 9$

Then substitute:

$f(3) = 2 \cdot 9 + 4 \cdot 3 + 12$

Simplify the expression:

$f(3) = 18 + 12 + 12$

Combine like terms:

$f(3) = 42$

So, $f(3) = 42$.

Would you like more details or have any other questions?

Here are 5 related questions to consider:

1. How do you find the value of a function for any given input?
2. What does the expression $2x^2 + 4x + 12$ represent graphically?
3. How do you find the vertex of a quadratic function like $f(x) = 2x^2 + 4x + 12$?
4. How do you determine if a quadratic function opens upwards or downwards?
5. How would you solve for $x$ if $f(x) = 0$?

Tip: Always remember to substitute the input value correctly and perform operations in the correct order (exponents, multiplication, addition).