Substitute \( x = -2 \): \( f(-2) = 2(-2)^2 - 3(-2) + 1 = 8 + 6 + 1 = 15 \).
["Substitute ( x = -2 ) into the Function: A Step-by-Step Evaluation", "Understanding function evaluation is fundamental in algebra, and one common task is substituting specific values into expressions or equations. This article explores how to efficiently substitute ( x = -2 ) into the function\n[\nf(x) = 2(-2)^2 - 3(-2) + 1\n]\nand why this substitution yields the value 15.", "---", "### Understanding the Expression", "The function given is:\n[\nf(x) = 2(-2)^2 - 3(-2) + 1\n]\nThis is a quadratic function expressed in explicit form. To compute ( f(-2) ), we replace every instance of ( x ) with (-2) and simplify using order of operations.", "At a glance, direct substitution results in:\n[\nf(-2) = 2(-2)^2 - 3(-2) + 1\n]", "---", "### Step-by-Step Substitution and Simplification", "1. Substitute ( x = -2 ):\n The expression becomes:\n [\n f(-2) = 2(-2)^2 - 3(-2) + 1\n ]\n Recall that exponents apply first, so ((-2)^2 = 4).", "2. Evaluate the squared term:\n [\n 2(-2)^2 = 2 \ imes 4 = 8\n ]", "3. Evaluate the multiplication:\n [\n -3(-2) = 6\n ]", "4. Add all the terms together:\n [\n f(-2) = 8 + 6 + 1 = 15\n ]", "---", "### Why This Simplification Matters", "This calculation illustrates a key algebraic skill:\n- Order of operations is crucial—successively evaluating exponents before multiplication, then handling negation.\n- Substitution transforms the function into a simple arithmetic expression, making it easy to compute.\n- Understanding such substitutions is foundational for solving equations, analyzing function behavior, and working with polynomials.", "---", "### Final Thoughts", "Substituting ( x = -2 ) into ( f(x) = 2(-2)^2 - 3(-2) + 1 ) leads to a clear result:\n[\nf(-2) = 15\n]\nThis process demonstrates how direct evaluation supports deeper mathematical reasoning, essential for students and anyone working with algebraic functions.", "---", "### TL;DR", "- Substitute ( x = -2 ) into ( f(x) = 2(-2)^2 - 3(-2) + 1 )\n- Compute step-by-step:\n ( 2(-2)^2 = 8 ), ( -3(-2) = 6 ), so:\n ( 8 + 6 + 1 = 15 )\n- Thus, ( f(-2) = 15 )", "Mastering such substitutions strengthens algebraic confidence and problem-solving skills.", "---", "Keywords: substitute x = -2, evaluate f(x), function evaluation, algebraic substitution, solve f(-2), mathematical steps, quadratic functions, order of operations"]
