y = -1/8x^2 + 2x + 29 The given equation models a company's scheduled deliveries over 8 months, where y...

1. INFER what the question is asking

• The question asks for interpretation of the y-intercept
• The y-intercept occurs when \(\mathrm{x = 0}\)
• I need to find this point and explain what it means in the delivery context

2. SIMPLIFY to find the y-intercept

• Substitute \(\mathrm{x = 0}\) into the equation:
  \(\mathrm{y = -\frac{1}{8}x^2 + 2x + 29}\)
  \(\mathrm{y = -\frac{1}{8}(0)^2 + 2(0) + 29}\)
  \(\mathrm{y = 0 + 0 + 29 = 29}\)
• The y-intercept is \(\mathrm{(0, 29)}\)

3. TRANSLATE the mathematical result into contextual meaning

• \(\mathrm{x = 0}\) means: 0 months after the end of May 2012
• 0 months after the end of May 2012 = the end of May 2012
• \(\mathrm{y = 29}\) means: 29 estimated scheduled deliveries
• Combined interpretation: At the end of May 2012, there were 29 estimated scheduled deliveries

Answer: B

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misinterpret what \(\mathrm{x = 0}\) represents in the time context. They might think "0 months after May" means the beginning of May, or they might incorrectly associate \(\mathrm{x = 0}\) with June instead of May. Some students also confuse whether they're looking at the end or beginning of months.

This may lead them to select Choice C or D (thinking about June instead of May) or become confused about the timing and guess.

The Bottom Line:

This problem tests whether students can bridge between mathematical concepts (y-intercept) and real-world interpretation. The mathematical calculation is straightforward, but translating "x months after the end of May 2012" requires careful attention to what \(\mathrm{x = 0}\) actually represents in time.