["Understanding the Function Evaluated at ( f(3) = 2(3)^2 - 3(3) + 1 ): Step-by-Step Breakdown", "Evaluating functions at specific input values is a foundational skill in algebra and calculus. One such expression we often analyze is:", "[
\nf(3) = 2(3)^2 - 3(3) + 1
\n]", "This article breaks down the step-by-step computation to find ( f(3) = 18 - 9 + 1 = 10 ), while highlighting key mathematical principles along the way.", "---", "### What Does It Mean to Evaluate ( f(3) )?", "When we write ( f(3) ), we substitute ( x = 3 ) into the input function ( f(x) ). This process allows us to calculate the actual output value corresponding to that input. For quadratic expressions like this one, evaluation helps reveal how the function behaves at particular points on a graph.", "---", "### Step 1: Substitute ( x = 3 ) into the Function", "Start with the given expression:
\n[
\nf(3) = 2(3)^2 - 3(3) + 1
\n]", "This combines a quadratic term ( 2(3)^2 ), a linear term ( -3(3) ), and a constant ( +1 ).", "---", "### Step 2: Calculate the Exponential Term", "First evaluate ( (3)^2 ):
\n[
\n(3)^2 = 9
\n]", "Now multiply by 2:
\n[
\n2 \cdot 9 = 18
\n]", "This step demonstrates how exponentiation influences the function’s growth—rapid increases here due to squaring.", "---", "### Step 3: Compute the Linear Term", "Next, calculate ( -3(3) ):
\n[
\n-3 \cdot 3 = -9
\n]", "Multiplying a variable by a negative constant introduces a decrease proportional to its value.", "---", "### Step 4: Add All Terms", "Now combine all results:
\n[
\nf(3) = 18 - 9 + 1
\n]", "Perform left-to-right addition and subtraction:
\n[
\n18 - 9 = 9
\n]
\n[
\n9 + 1 = 10
\n]", "So,
\n[
\nf(3) = 10
\n]", "---", "### Why This Matters: Practical Applications of Function Evaluation", "Evaluating functions at specific values helps model real-world scenarios—such as calculating profit, physics motion, or growth rates. Understanding these computations lays the groundwork for more advanced topics like derivatives, integrals, and function analysis.", "---", "### Final Summary", "Evaluating ( f(3) = 2(3)^2 - 3(3) + 1 ):
\n- Substitutes ( x = 3 )
\n- Applies exponentiation, multiplication, and addition/subtraction
\n- Results in ( f(3) = 10 )", "This simple computation exemplifies how algebraic expressions translate into concrete numerical outcomes.", "---", "Key Takeaway: Mastering function evaluation builds critical problem-solving skills essential in mathematics, science, and engineering.", "---", "Keywords for SEO:
\n- Evaluate ( f(3) ) step-by-step
\n- How to compute ( 2(3)^2 - 3(3) + 1 )
\n- Function evaluation explained
\n- Step-by-step math problem solving
\n- Algebraic computation tutorial
\n- Solving quadratic expressions at specific points", "Meta Description:
\nLearn how to evaluate ( f(3) = 2(3)^2 - 3(3) + 1 ) step-by-step—calculating exponentiation, multiplication, and addition to find ( f(3) = 10 ). Perfect for algebra students and math beginners."]
