If the function \( f(x) = 3x^2 - 2x + 1 \), find \( f(2) \).

["Finding ( f(2) ) for the Function ( f(x) = 3x^2 - 2x + 1 ): A Step-by-Step Guide", "Understanding how to evaluate functions at specific values is a fundamental skill in algebra and calculus. One common task is finding ( f(2) ) for a given quadratic function. In this article, we’ll walk through how to compute ( f(2) ) for the function\n[ f(x) = 3x^2 - 2x + 1 ], using a clear, step-by-step approach that enhances comprehension and helps with future problem-solving.", "---", "### What Does It Mean to Find ( f(2) )?", "To find ( f(2) ), we substitute ( x = 2 ) into the function in place of every occurrence of ( x ). This means plugging the number 2 into the formula and simplifying step by step using order of operations to ensure accuracy.", "---", "### Step 1: Write the Function with ( x = 2 )", "Start with the original function:\n[ f(x) = 3x^2 - 2x + 1 ]\nSubstitute ( x = 2 ):\n[ f(2) = 3(2)^2 - 2(2) + 1 ]", "---", "### Step 2: Apply the Exponent", "Evaluate the squared term first:\n[ 2^2 = 4 ]\nNow multiply by the coefficient:\n[ 3 \ imes 4 = 12 ]\nSo the expression becomes:\n[ f(2) = 12 - 2(2) + 1 ]", "---", "### Step 3: Perform Multiplication", "Now compute:\n[ -2(2) = -4 ]\nNow the expression is:\n[ f(2) = 12 - 4 + 1 ]", "---", "### Step 4: Apply Addition and Subtraction from Left to Right", "First subtract:\n[ 12 - 4 = 8 ]\nThen add:\n[ 8 + 1 = 9 ]", "---", "### Final Result", "[ f(2) = 9 ]", "---", "### Why This Matters: Applications of Function Evaluation", "Knowing how to evaluate functions like ( f(x) = 3x^2 - 2x + 1 ) at specific points is essential in many real-world contexts:", "- Physics: Calculating position or velocity at a given time\n- Economics: Estimating profit at a certain number of units sold\n- Engineering: Modeling heat distribution or structural stress\n- Machine Learning: Predicting outcomes at specific input values", "Mastering function evaluation helps lay the foundation for advanced topics in mathematics and science.", "---", "### Quick Recap: Evaluating ( f(2) )", "- Substitute: ( f(2) = 3(2)^2 - 2(2) + 1 )\n- Compute exponent: ( 3(4) - 4 + 1 )\n- Multiply: ( 12 - 4 + 1 )\n- Add: ( f(2) = 9 )", "---", "In conclusion, evaluating a function at a particular input is straightforward when following the correct order of operations. With practice, you’ll reliably compute ( f(2) ) for any quadratic expression efficiently.", "---", "Key SEO Keywords:\n- Evaluate ( f(2) )\n- How to find ( f(2) )\n- Function evaluation tutorial\n- Step-by-step quadratic function\n- Calculate ( f(2) )\n- Algebra fundamentals", "Optimizing your understanding of function evaluation boosts both academic performance and practical problem-solving skills—an essential part of mastering algebra!"]