Substitute \( x = 2 \): \( f(2) = 3(2)^2 - 2(2) + 1 = 12 - 4 + 1 = 9 \).
["Understanding Substitute ( x = 2 ) in the Function ( f(x) = 3x^2 - 2x + 1 ): A Step-by-Step Explanation", "When working with functions in algebra, substitution is a fundamental technique that allows us to evaluate a function at specific values. One common substitution is replacing ( x ) with a simple number—such as ( x = 2 )—to compute outputs efficiently. Let’s explore how substituting ( x = 2 ) into the function ( f(x) = 3x^2 - 2x + 1 ) works step-by-step, arriving at the result ( f(2) = 9 ).", "### What Does ( f(2) ) Mean?", "The expression ( f(2) ) means we are evaluating the function ( f ) at the input value ( x = 2 ). To find ( f(2) ), we substitute ( 2 ) in place of every occurrence of ( x ) in the function’s formula.", "### Step-by-Step Evaluation", "Start with the original function:\n[\nf(x) = 3x^2 - 2x + 1\n]", "Now substitute ( x = 2 ):\n[\nf(2) = 3(2)^2 - 2(2) + 1\n]", "Break it down:", "1. Evaluate the exponent:\n [\n (2)^2 = 4\n ]\n So,\n [\n 3(2)^2 = 3 \ imes 4 = 12\n ]", "2. Evaluate the linear term:\n [\n -2(2) = -4\n ]", "3. Combine all parts:\n Now substitute each computed value back:\n [\n f(2) = 12 - 4 + 1\n ]", "4. Perform the arithmetic:\n [\n 12 - 4 = 8\n ]\n [\n 8 + 1 = 9\n ]", "### Final Result", "[\nf(2) = 9\n]", "This confirms that when the input ( x = 2 ) is used in the function ( f(x) = 3x^2 - 2x + 1 ), the output is exactly 9.", "### Why This Operation Matters", "Substitute ( x = 2 ) into a function is useful in many contexts:\n- Solving for specific outputs\n- Checking properties like roots or maximum/minimum values\n- Plotting functions by evaluating key points\n- Applying mathematical models at concrete inputs", "Understanding how to properly substitute values allows students and professionals alike to analyze functions accurately and efficiently.", "---", "Key Takeaways:\n- Substituting ( x = 2 ) means replacing every ( x ) with 2 in the expression.\n- Order of operations (exponents first, then multiplication, then addition/subtraction) ensures correct calculation.\n- ( f(2) = 9 ) validates the function’s behavior at input ( x = 2 ).\n- Mastering substitution supports deeper algebraic problem-solving.", "---", "Try it Yourself:\nNext time you see ( f(x) ), practice substituting values like ( x = 2 ), ( x = -1 ), or even random integers to build confidence and intuition.", "---", "Summary:\nSubstitute ( x = 2 ) into ( f(x) = 3x^2 - 2x + 1 ) → result is ( f(2) = 9 ). This simple evaluation illustrates a core algebra skill essential for understanding functions and their real-world applications.", "---", "Meta Title:\nSubstitute ( x = 2 ) into ( f(x) = 3x^2 - 2x + 1 ): Step-by-Step Calculation", "Meta Description:\nLearn how to substitute ( x = 2 ) into the function ( f(x) = 3x^2 - 2x + 1 ) and correctly compute ( f(2) = 9 ). A beginner-friendly guide with clear steps.", "Keywords:\nsubstitute ( x = 2 ), ( f(2) ), function evaluation, algebraic substitution, ( f(x) = 3x^2 - 2x + 1 ), step-by-step math, solving functions."]
