First, calculate $ f(4) = 3(4)^2 + 2(4) + 1 = 48 + 8 + 1 = 57 $.

["Calculating $ f(4) = 3(4)^2 + 2(4) + 1 $: A Simple Guide to Function Evaluation", "Understanding how to evaluate functions is a foundational skill in mathematics and computer science. Today, we explore a clear example: calculating $ f(4) = 3(4)^2 + 2(4) + 1 $. This step-by-step breakdown will help you master function evaluation, while highlighting its importance in real-world problem solving.", "### What is $ f(4) $?", "The expression $ f(4) $ means we substitute the input $ 4 $ into the function $ f $. Depending on the function definition, $ f(x) $ typically represents a mathematical relationship that can involve addition, multiplication, exponents, and constants.", "### Step-by-Step Calculation of $ f(4) $", "Let’s compute $ f(4) $ using the given function:", "$$\nf(4) = 3(4)^2 + 2(4) + 1\n$$", "#### Step 1: Evaluate the exponent\n$$\n(4)^2 = 16\n$$\nNow the function becomes:\n$$\nf(4) = 3 \cdot 16 + 2(4) + 1\n$$", "#### Step 2: Perform multiplication\n$$\n3 \cdot 16 = 48\n\quad \ ext{and} \quad\n2 \cdot 4 = 8\n$$\nResulting in:\n$$\nf(4) = 48 + 8 + 1\n$$", "#### Step 3: Add all terms\n$$\n48 + 8 = 56\n\Rightarrow 56 + 1 = 57\n$$", "### Final Answer\n$$\nf(4) = 57\n$$", "### Why This Matters", "Evaluating functions like $ f(4) $ is essential in algebra, calculus, engineering, and programming. Functions model real-life relationships—from predicting growth, calculating costs, to controlling systems in robotics. Mastering these calculations enables understanding more complex models, such as polynomial regression, physics simulations, or algorithm efficiency analysis.", "### Conclusion", "Breaking down $ f(4) = 3(4)^2 + 2(4) + 1 $ step-by-step demystifies function evaluation. By applying order of operations—exponents first, then multiplication, followed by addition—you efficiently arrive at $ f(4) = 57 $. Practice this technique to build strong mathematical foundations and apply it confidently across diverse fields.", "---", "Keywords: evaluate function, calculate $ f(4) $, $ f(x) = 3x^2 + 2x + 1 $, exponentiation, algebraic simplification, step-by-step math, function example, polynomial evaluation.\nMeta Description: Learn how to calculate $ f(4) = 3(4)^2 + 2(4) + 1 $ step-by-step, with clear explanations and real-world relevance in mathematics and STEM fields."]