Substituting \( x = 2 \) into the function, \( f(2) = 3(2)^2 - 12(2) + 7 = 12 - 24 + 7 = -5 \).
["# Understanding Function Evaluation: Substituting ( x = 2 ) into ( f(x) = 3x^2 - 12x + 7 )", "When working with polynomial functions, evaluating the function at a specific value of ( x ) is a fundamental skill in algebra and calculus. One common substitution is replacing ( x ) with a number—such as ( x = 2 )—to find ( f(2) ). This process helps students and professionals alike grasp how functions behave at particular points.", "In this article, we explore how to substitute ( x = 2 ) into the function:", "[\nf(x) = 3x^2 - 12x + 7\n]", "and compute ( f(2) ) step-by-step.", "## Step 1: Substitute ( x = 2 ) into the Function", "Begin by replacing every instance of ( x ) in the function with 2:", "[\nf(2) = 3(2)^2 - 12(2) + 7\n]", "## Step 2: Evaluate the Exponent", "Next, calculate the exponent inside the parentheses:", "[\n(2)^2 = 4\n]", "Now replace it back into the expression:", "[\nf(2) = 3(4) - 12(2) + 7\n]", "## Step 3: Perform Multiplication", "Multiply each term:", "[\n3 \ imes 4 = 12\n]\n[\n-12 \ imes 2 = -24\n]", "Now the expression becomes:", "[\nf(2) = 12 - 24 + 7\n]", "## Step 4: Perform Addition and Subtraction from Left to Right", "Start with the first two terms:", "[\n12 - 24 = -12\n]", "Then add 7:", "[\n-12 + 7 = -5\n]", "## Final Result", "[\nf(2) = -5\n]", "## Why This Matters", "Substituting values into functions is essential in graphing, modeling real-world situations, optimizing solutions, and understanding function behavior. Evaluating ( f(2) = -5 ) gives the exact output of the function at ( x = 2 ), allowing for precise analysis.", "## Summary", "- Function: ( f(x) = 3x^2 - 12x + 7 )\n- Substitute: ( x = 2 )\n- Compute: ( f(2) = 3(2)^2 - 12(2) + 7 = 12 - 24 + 7 = -5 )\n- Result: ( f(2) = -5 )", "Mastering function substitution equips learners with a powerful tool to analyze and apply mathematical models confidently. Whether solving equations, studying curves, or applying calculus, this skill remains indispensable.", "---", "Keywords for SEO:\nfunction evaluation, substitute ( x = 2 ), compute ( f(2) ), define ( f(x) = 3x^2 - 12x + 7 ), step-by-step function substitution, algebra tutorial, solving for ( f(2) ), polynomial function, mathematical computation", "Meta Description:\nLearn how to substitute ( x = 2 ) into the function ( f(x) = 3x^2 - 12x + 7 ) with step-by-step calculation. Discover why evaluating functions at specific points is essential in algebra and calculus."]
