If \(f(x) = x^2 - 4x + 4\), find \(f(3)\).
["# How to Calculate (f(3)) for the Quadratic Function (f(x) = x^2 - 4x + 4)", "Understanding how to evaluate a function at a specific input value is a foundational skill in algebra. In this article, we’ll walk through the step-by-step process of finding (f(3)) for the quadratic function:", "[\nf(x) = x^2 - 4x + 4\n]", "Whether you're a student, educator, or someone brushing up on algebra, mastering this concept helps strengthen your mathematical foundation—especially when dealing with polynomial functions like quadratics.", "## What Does It Mean to Find (f(3))?", "When we write (f(3)), we replace every occurrence of (x) in the function (f(x)) with the number 3. This gives us:", "[\nf(3) = (3)^2 - 4(3) + 4\n]", "This expression represents the output of the function when (x = 3), which we can evaluate using basic arithmetic.", "## Step-by-Step Evaluation", "Now, let’s simplify the expression step by step:", "1. Substitute (x = 3):", "[\nf(3) = (3)^2 - 4(3) + 4\n]", "2. Evaluate the exponent:", "[\n(3)^2 = 9\n]", "3. Perform multiplication:", "[\n4(3) = 12\n]", "4. Rewrite the expression with computed values:", "[\nf(3) = 9 - 12 + 4\n]", "5. Simplify from left to right:", "[\n9 - 12 = -3\n]\n[\n-3 + 4 = 1\n]", "## Final Result", "[\nf(3) = 1\n]", "This means that the function (f(x) = x^2 - 4x + 4) evaluates to 1 when (x = 3).", "## Why This Matters", "Calculating (f(3)) is more than just plugging numbers into a formula. It helps explore function behavior, solve equations, and apply algebra in real-world modeling—such as predicting outcomes, optimizing resources, or analyzing geometric shapes defined by quadratic equations.", "## Practice Tip", "Try computing (f(0)), (f(1)), and (f(2)) using the same method to reinforce your understanding. Understanding how small changes in (x) affect (f(x)) deepens your intuition for polynomial functions.", "---", "Summary:\nFor the function (f(x) = x^2 - 4x + 4), evaluating (f(3)) yields:", "[\nf(3) = 1\n]", "Analysis of quadratic functions at specific points is essential for deepening algebraic proficiency."]
