An egg is thrown from a rooftop. The equation h = -4.9t^2 + 9t + 18 represents this situation, where...

1. TRANSLATE the problem information

• Given equation: \(\mathrm{h = -4.9t^2 + 9t + 18}\)
• Variables: \(\mathrm{h}\) = height above ground (meters), \(\mathrm{t}\) = time after throwing (seconds)
• Question asks: height from which egg was thrown

2. TRANSLATE what "height from which egg was thrown" means

• This asks for the height at the very beginning - the moment of throwing
• At the moment of throwing, \(\mathrm{t = 0}\) (zero seconds have passed)
• So we need to find \(\mathrm{h}\) when \(\mathrm{t = 0}\)

3. SIMPLIFY by substituting \(\mathrm{t = 0}\) into the equation

• \(\mathrm{h = -4.9t^2 + 9t + 18}\)
• \(\mathrm{h = -4.9(0)^2 + 9(0) + 18}\)
• \(\mathrm{h = 0 + 0 + 18}\)
• \(\mathrm{h = 18}\)

Answer: 18 meters

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misinterpret "height from which the egg was thrown" to mean the maximum height the egg reaches during its flight.

They might try to find when the derivative equals zero or look for the vertex of the parabola, leading to complex calculations that don't answer the actual question. This leads to confusion and potentially selecting an incorrect answer or abandoning the systematic approach.

Second Most Common Error:

Conceptual confusion about initial conditions: Students don't realize that \(\mathrm{t = 0}\) represents the starting moment and might think they need to solve for when \(\mathrm{h = 0}\) (when the egg hits the ground) instead.

This backward thinking leads them away from the simple substitution needed and toward solving a quadratic equation unnecessarily.

The Bottom Line:

This problem tests whether students can TRANSLATE a real-world description into the correct mathematical operation. The key insight is recognizing that "initial condition" problems almost always mean "substitute \(\mathrm{t = 0}\)."