\[ f(3) = 2(3)^2 - 3(3) + 1 = 2 \times 9 - 9 + 1 = 18 - 9 + 1 = 10 \]

["### Solving ( f(3) = 2(3)^2 - 3(3) + 1 ): Step-by-Step Explanation", "Understanding how to evaluate expressions like ( f(3) = 2(3)^2 - 3(3) + 1 ) is fundamental in algebra. This particular problem demonstrates the application of order of operations, exponentiation, multiplication, and basic addition and subtraction to compute function values. In this article, we break down the full calculation step-by-step to help students and enthusiasts master function evaluation.", "---", "#### Step 1: Understand the Function", "The expression ( f(3) = 2(3)^2 - 3(3) + 1 ) represents a function ( f(x) ) evaluated at ( x = 3 ).\n- The expression inside is a quadratic function with:\n - A squared term: ( 2(3)^2 )\n - A linear term: ( -3(3) )\n - A constant term: ( +1 )", "---", "#### Step 2: Apply Order of Operations — PEMDAS/BODMAS", "Remember the order:\nParentheses, Exponents (or Orders), Multiplication and Division (left to right), Addition and Subtraction (left to right).", "---", "Step 2.1: Evaluate the exponent\n( (3)^2 = 9 )", "Now substitute:\n[\nf(3) = 2 \ imes 9 - 3 \ imes 3 + 1\n]", "---", "Step 2.2: Perform the multiplications\n- ( 2 \ imes 9 = 18 )\n- ( 3 \ imes 3 = 9 )", "The expression simplifies to:\n[\nf(3) = 18 - 9 + 1\n]", "---", "Step 2.3: Perform subtraction and addition from left to right\n- First, ( 18 - 9 = 9 )\n- Then, ( 9 + 1 = 10 )", "---", "#### Final Result\n[\nf(3) = 10\n]", "---", "### Why This Matters", "Evaluating polynomial functions like ( f(x) ) is essential in algebra, calculus, and applied mathematics. Mastering expressions involving exponents and linear terms helps in solving equations, graphing functions, and modeling real-world scenarios.", "If you're learning algebra, practice such expressions regularly — they build a strong foundation for higher-level math topics.", "---", "#### Summary", "Given:\n[\nf(3) = 2(3)^2 - 3(3) + 1\n]", "Using exponent first:\n[\n= 2 \ imes 9 - 9 + 1 = 18 - 9 + 1 = 10\n]", "(\boxed{f(3) = 10})", "---", "Keywords: evaluate ( f(3) ), polynomial evaluation, algebra math explanation, solving quadratic expressions, step-by-step math tutorial, exponent rules, order of operations", "Meta Description: Step-by-step explanation of evaluating ( f(3) = 2(3)^2 - 3(3) + 1 ), showing exponentiation, multiplication, and order of operations to arrive at ( f(3) = 10 ). Perfect for students learning function evaluation and algebra basics."]