f(-2) = 3(-2)^2 - 4(-2) + 2 = 3(4) + 8 + 2 = 12 + 8 + 2 = 22.

["### Understanding the Expression: f(−2) = 3(−2)² − 4(−2) + 2 — Step-by-Step Evaluation", "Exploring mathematical expressions can turn abstract algebra into an engaging, rewarding experience. One such example is evaluating the function:", "[\nf(-2) = 3(-2)^2 - 4(-2) + 2\n]", "In this article, we’ll break down this quadratic expression step by step, explaining how to evaluate it at ( x = -2 ), why each operation matters, and how mastering these techniques strengthens your algebra skills.", "---", "#### Step 1: Simplify the Exponent—Recognizing the Square Term", "The expression begins with ( 3(-2)^2 ). This is a key growth area—exponents apply before multiplication. The expression ((-2)^2) means (-2) multiplied by itself:", "[\n(-2)^2 = (-2) \ imes (-2) = 4\n]", "This results in:", "[\n3(-2)^2 = 3 \ imes 4 = 12\n]", "✅ Key Insight: Squaring removes the negative sign because a negative times a negative gives a positive. Always prioritize exponents before multiplication.", "---", "#### Step 2: Handle the Negation — Evaluating Multiply-by-Negative Terms", "Next, evaluate the term (-4(-2)). This is straightforward multiplication:", "[\n-4(-2) = (-4) \ imes (-2) = 8\n]", "✅ Key Insight: Multiplying two negative numbers produces a positive result. The double negative removes the negative, turning (-(-2)) into (+2), scaled by (-4).", "---", "#### Step 3: Add the Constant Term", "The final term is simply the constant (+2), which stays unchanged:", "[\n+2\n]", "---", "#### Putting It All Together", "Now combine all simplified components:", "[\nf(-2) = 3(-2)^2 - 4(-2) + 2 = 12 + 8 + 2 = 22\n]", "✅ Final Answer:\n[\nf(-2) = 22\n]", "---", "#### Why This Format Matters — Syntax in Polynomial Evaluation", "This example highlights a common polynomial format:", "[\nf(x) = ax^2 + bx + c\n]", "In this case:", "- The ( 3(-2)^2 ) evaluates the quadratic component,\n- The ( -4(-2) ) captures a linear term,\n- The ( +2 ) is a constant offset.", "Understanding how each term transforms the input ( x = -2 ) helps build intuition for solving equations, graphing functions, and applying algebra algebraically in real-world problems.", "---", "#### Pro Tips for Algebra Success", "- Order of Operations Matters: Always follow PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction).\n- Sign Changes: Remember:\n - Negative × Negative = Positive\n - Negative × Positive = Negative\n- Use Parentheses for Clarity: Especially in complex expressions, grouping terms prevents errors.", "---", "#### Conclusion", "Evaluating expressions like ( f(-2) = 3(-2)^2 - 4(-2) + 2 ) is more than just plug-and-chug—it’s a foundation for mastering functions, solving equations, and understanding quadratic behavior. By breaking each step carefully, you build both accuracy and confidence in algebra.", "Whether you’re a student learning the basics or simply refreshing your skills, mastering expression evaluation opens doors to deeper mathematical insight.", "---", "Keywords: evaluate f(-2), polynomial evaluation, exponent rules, algebra steps, solve quadratic expressions, step-by-step math, function evaluation, algebra practice"]