\(a_2 = 3(2)^2 + 2(2) + 1 = 17\)
["Understanding the Expression ( a_2 = 3(2)^2 + 2(2) + 1 = 17 ): A Clear Breakdown", "When encountering the algebraic expression ( a_2 = 3(2)^2 + 2(2) + 1 ), many students and learners seek a clear explanation of how it simplifies to 17. This equation represents a crucial stepping stone in quadratic expressions and polynomial evaluation, playing an important role in algebra for both education and practical problem-solving.", "### What Does ( a_2 ) Represent?", "In algebra, ( a_2 ) typically refers to a term involving a quadratic component. Here, it stands for an expression evaluated specifically at ( x = 2 ), forming a well-known quadratic function in standard form:\n[ a_2 = 3x^2 + 2x + 1 ]\nEvaluating this quadratic at ( x = 2 ) gives:\n[\na_2 = 3(2)^2 + 2(2) + 1\n]", "### Step-by-Step Evaluation", "Let’s break down each component:", "1. Squaring the Input Value:\n Start with ( (2)^2 ), which equals 4.\n Multiply by 3:\n [\n 3 \ imes 4 = 12\n ]", "2. Linear Term Evaluation:\n Multiply ( 2 \ imes 2 = 4 ).", "3. Adding the Constant:\n The constant term is simply 1.", "4. Combine All Parts:\n Add the results from each step:\n [\n 12 + 4 + 1 = 17\n ]", "### Why Is This Important?", "Understanding how to evaluate expressions like ( a_2 = 3x^2 + 2x + 1 ) at specific values is foundational for:\n- Solving quadratic equations analytically and numerically\n- Modeling real-world phenomena such as projectile motion\n- Developing skills in function evaluation, essential for calculus and beyond", "### Final Result", "Thus, confirming the algebraic identity:\n[\n\boxed{ a_2 = 3(2)^2 + 2(2) + 1 = 12 + 4 + 1 = 17 }\n]\nThis calculation demonstrates not only basic arithmetic and exponent rules but also highlights the power of polynomial functions in expressing relationships between variables.", "---", "Keywords for SEO Optimization:\n- Evaluate quadratic expression ( 3x^2 + 2x + 1 ) at ( x = 2 )\n- Solve ( a_2 = 3(2)^2 + 2(2) + 1 )\n- How to calculate ( 3x^2 + 2x + 1 = 17 )\n- Algebraic evaluation for beginners\n- Understanding polynomial functions ( a_2(x) )", "By simplifying step-by-step and explaining each element, learners gain clarity on both computation and conceptual relevance, supporting deeper mastery of algebra."]
