$ y = -(3)^2 + 6(3) + 1 = -9 + 18 + 1 = 10 $.
["Understanding the Equation: y = -(3)² + 6(3) + 1 Explained", "Mathematics often presents us with elegant expressions that, once simplified, reveal clear values and fascinating insights. One such equation is:", "[\ny = -(3)^2 + 6(3) + 1\n]", "At first glance, this may seem straightforward, but breaking it down step-by-step not only confirms its solution—yielding ( y = 10 )—but also deepens our understanding of algebraic operations and order of operations.", "### Step-by-Step Breakdown", "Let’s evaluate the expression carefully using the order of operations (PEMDAS/BODMAS):", "1. Exponentiation (P - Parentheses, E - Exponents first):\n Start with (-(3)^2):\n [\n (3)^2 = 9 \Rightarrow -(3)^2 = -9\n ]", "2. Multiplication (Next operations from left to right):\n [\n 6(3) = 18\n ]", "3. Addition:\n Now combine all parts:\n [\n y = -9 + 18 + 1\n ]\n First, (-9 + 18 = 9), then:\n [\n 9 + 1 = 10\n ]", "Thus, the final result is\n[\ny = 10\n]", "### Why This Equation Matters", "This expression is a powerful example of applying arithmetic in algebra. It demonstrates how negative signs, exponents, and multiplication interact cohesively. Such problems are common in high school-level algebra, building foundational skills needed for more complex functions.", "Moreover, understanding how to simplify expressions like ( y = -(3)^2 + 6(3) + 1 ) strengthens problem-solving abilities essential in STEM fields, computer science, and everyday calculations involving quadratic trends.", "### Real-World Applications", "Equations of this form appear in various scenarios:\n- Physics: Calculating motion trajectories or energy equations.\n- Engineering: Modeling structural loads and stress factors.\n- Economics: Analyzing profit and cost relationships.", "While this specific equation models a simple quadratic result, similar algebraic structures underpin advanced modeling across disciplines.", "### Final Notes", "Mastering expressions like ( y = -(3)^2 + 6(3) + 1 ) is key to fluency in algebra. Once simplified, ( y = 10 ) becomes not just a number but a meaningful outcome rooted in proper mathematical reasoning.", "Next time you encounter a quadratic-style expression, remember—follow the order of operations carefully, and you’ll uncover the truth hidden within.", "---", "Keywords for SEO:\n- Simplify quadratic equation\n- Solve y = -(3)^2 + 6(3) + 1\n- Algebraic expression explained\n- Step-by-step equation solving\n- Value of y = -(3)² + 6(3) + 1\n- Order of operations mathematics", "Meta Description:\nSimplify and solve ( y = -(3)^2 + 6(3) + 1 ) step by step. Learn how exponents, multiplication, and addition combine to yield ( y = 10 )—a clear example of algebraic fluency."]
