b(9) = 9^2 - 3(9) + 5 = 81 - 27 + 5 = 59

["# Understanding the Quadratic Expression: b(9) = 9² – 3(9) + 5 = 59", "When exploring functional expressions in algebra, one common approach is substituting specific values into formulas to evaluate their outcomes. Take the equation:", "b(9) = 9² – 3(9) + 5", "This expression combines squaring, multiplication, and addition to evaluate what “b” equals when the input is 9. Breaking it down step-by-step not only clarifies the calculation but also reinforces fundamental algebra skills.", "## Step-by-Step Evaluation", "Start by evaluating each term according to the order of operations (PEMDAS/BODMAS):", "1. Square the base:\n ( 9² = 81 )", "2. Multiply:\n ( 3 \ imes 9 = 27 )", "3. Substitute and simplify:\n Replace into the original expression:\n ( b(9) = 81 - 27 + 5 )", "4. Perform subtraction and addition from left to right:\n - ( 81 - 27 = 54 )\n - ( 54 + 5 = 59 )", "Therefore,\nb(9) = 59", "## Why This Matters in Algebra", "Expressions like b(9) illustrate how functions map inputs (in this case, 9) to a specific output through arithmetic rules. This concept forms the backbone of deeper topics, including quadratic functions, graph transformations, and real-world problem modeling.", "While ( b(x) = x² - 3x + 5 ) is a quadratic function with vertex and axis of symmetry properties, evaluating at ( x = 9 ) shows a concrete numerical result. Mastery of such substitutions strengthens algebraic intuition and prepares learners for more complex calculations and functions.", "## Practical Applications of Evaluating Polynomial Expressions", "Beyond classroom exercises, computing expressions like b(9) mirrors tasks in finance (profit predictions), physics (motion equations), and programming (algorithm evaluation). Quick mental math or calculator use for such formulas helps solve real-life problems efficiently.", "---", "In summary, evaluating ( b(9) = 9² - 3(9) + 5 ) provides a clear, correct result of 59 — reinforcing core arithmetic skills essential for algebra and beyond."]