f(3) = 3(3)^2 + 2(3) - 5 = 3 \times 9 + 6 - 5 = 27 + 6 - 5 = 28

["# Understanding the Mathematical Expression: f(3) = 3(3)² + 2(3) - 5 = 28", "When solving math problems involving functions, evaluating expressions at specific values is a fundamental concept. In this article, we’ll break down the function evaluation of ( f(3) = 3(3)^2 + 2(3) - 5 ), step by step, explaining each part to help you understand how we arrive at the final result: 28. Whether you're a student learning algebra or someone exploring foundational mathematics, mastering this process is essential.", "## What is f(3)? Evaluating a Function at x = 3", "In mathematics, a function like ( f(x) ) assigns a unique output to each input value. Here, we are specifically evaluating the function at ( x = 3 ), meaning we substitute 3 into every occurrence of ( x ). The expression:", "[\nf(3) = 3(3)^2 + 2(3) - 5\n]", "represents the function output when ( x = 3 ). This evaluation process combines order of operations, exponentiation, multiplication, and arithmetic to compute the final numerical result.", "## Breaking Down the Expression Step by Step", "To solve ( f(3) = 3(3)^2 + 2(3) - 5 ), follow the standard order of operations—often remembered by PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction):", "### Step 1: Evaluate the exponent", "The expression includes ( (3)^2 ), which means 3 raised to the power of 2:\n[\n(3)^2 = 9\n]\nSo now the expression becomes:\n[\nf(3) = 3 \ imes 9 + 2(3) - 5\n]", "### Step 2: Perform multiplication", "Next, compute the multiplications:", "- ( 3 \ imes 9 = 27 )\n- ( 2 \ imes 3 = 6 )", "Now substitute these back:\n[\nf(3) = 27 + 6 - 5\n]", "### Step 3: Apply addition and subtraction from left to right", "Now combine the terms:\n- First, add: ( 27 + 6 = 33 )\n- Then subtract: ( 33 - 5 = 28 )", "Thus,\n[\nf(3) = 28\n]", "## Why This Process Matters", "Evaluating functions at specific inputs is crucial in algebra, calculus, and applied mathematics. It allows you to:\n- Predict outcomes based on variable inputs\n- Model real-world problems (e.g., motion, cost, growth)\n- Analyze functions by plugging in values instead of solving symbolic equations", "Understanding each step—especially exponentiation and correct operation order—ensures accuracy and deepens mathematical fluency.", "## Final Summary", "Evaluating ( f(3) = 3(3)^2 + 2(3) - 5 ) reveals that the function returns 28, verified through orderly computation: exponentiation, multiplication, and left-to-right addition/subtraction. Mastering these basics empowers you to tackle more complex algebraic expressions and real-world mathematical modeling with confidence.", "---", "This structured approach to evaluating functions not only delivers the correct result but also strengthens problem-solving skills essential for advanced math learners. Whether solving equations or designing applications, clarity in calculation ensures accurate and meaningful results."]