The function f is defined by \(\mathrm{f(x) = 10x^2 - 32x - 152}\). What is the value of \(\mathrm{f(0)}\)?

1. TRANSLATE the problem information

• Given information:
  • Function: \(\mathrm{f(x) = 10x^2 - 32x - 152}\)
  • Need to find: \(\mathrm{f(0)}\)

• What this tells us: We need to substitute \(\mathrm{x = 0}\) into the function definition

2. SIMPLIFY through substitution

• Substitute \(\mathrm{x = 0}\) into \(\mathrm{f(x) = 10x^2 - 32x - 152}\):

\(\mathrm{f(0) = 10(0)^2 - 32(0) - 152}\)

• Work through each term:
  • \(\mathrm{10(0)^2 = 10(0) = 0}\)
  • \(\mathrm{32(0) = 0}\)
  • The constant term -152 stays the same

• Combine the results:

\(\mathrm{f(0) = 0 - 0 - 152 = -152}\)

Answer: A. -152

Why Students Usually Falter on This Problem

Most Common Error Path:

Conceptual confusion about function notation: Students may not understand what \(\mathrm{f(0)}\) means or how to evaluate a function at a specific value.

Some students might think \(\mathrm{f(0)}\) means "multiply f by 0" or get confused about whether they should use 0 or some other approach. Without understanding that \(\mathrm{f(0)}\) simply means "substitute \(\mathrm{x = 0}\) into the function," they can't begin the problem systematically.

This leads to confusion and guessing among the answer choices.

The Bottom Line:

This problem tests the fundamental concept of function evaluation. Success depends entirely on understanding that \(\mathrm{f(0)}\) means substituting \(\mathrm{x = 0}\) into the function definition, then carefully working through the arithmetic. The calculation itself is straightforward once students grasp this core concept.