f\left(-\frac{3}{2}\right) = 4\left(-\frac{3}{2} + \frac{3}{2}\right)^2 = 4 \cdot 0 = 0

February 22, 2026

$f\left(-\frac{3}{2}\right) = 4\left(-\frac{3}{2} + \frac{3}{2}\right)^2 = 4 \cdot 0 = 0$

Understanding the Mathematical Expression: f(–3/2) = 4(–3/2 + 3/2)² = 0

Mathematics often reveals elegant simplicity beneath seemingly complex expressions. One such example is the function evaluation: f(–3/2) = 4(–3/2 + 3/2)² = 0

At first glance, this equation may appear puzzling, but careful analysis uncovers its underlying logic. This article explains step-by-step how and why this expression simplifies to 0, showing the power of basic algebraic operations.

The Function: Step-by-Step Breakdown

The function f(x) at x = –3/2 is defined by the formula:

f(–3/2) = 4(–3/2 + 3/2)²

Let’s simplify the expression inside the parentheses:

–3/2 + 3/2 = 0

This is simply the sum of a number and its inverse on the number line—thingally zero.

Evaluating the Square

Next, we square the result:

(–3/2 + 3/2)² = 0² = 0

Since any number squared equal to zero remains zero, this directly yields:

f(–3/2) = 4 × 0 = 0

Why This Matters

This example demonstrates a foundational principle in algebra: when an expression inside parentheses evaluates to zero, squaring it results in zero—then scaling by any real number (in this case, 4) preserves this property.

In broader terms, such evaluations help identify roots of functions, test symmetry, or simplify complex expressions in calculus and engineering.

Summary

Input: x = –3/2
Simplify: –3/2 + 3/2 = 0
Square: 0² = 0
Multiply: 4 × 0 = 0

Thus, f(–3/2) = 0 confirms how symmetry and zero values elegantly reduce complicated-looking expressions to a single truth.

Keep Learning

Understanding how operations like addition, squaring, and multiplication interact within functions empowers students and professionals alike. This simple calculation embodies the clarity and beauty of fundamental mathematics—perfect for learners, teachers, and math enthusiasts exploring core concepts.

Keywords: f(–3/2), mathematical evaluation, algebraic simplification, zero result, function analysis, mathematical examples, algebra tutorial, derivative simplification, calculus basics

Meta Description: Learn how f(–3/2) = 4(–3/2 + 3/2)² simplifies to zero through step-by-step algebra, revealing the power of evaluating expressions and zero operations in functions. Perfect guide for math students and educators.