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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).

Use the following function rule to find f(3). f(x) = 2x^2 + 4x + 12

Learn how to find the value of a function for a given input. This problem focuses on evaluating the quadratic function f(x) = 2x^2 + 4x + 12 at x = 3. Suitable for students in Grades 8-10, this solution explains the process of substitution and step-by-step calculations.

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