GED Mathematical Reasoning TestAlgebraic Problem Solving with Expressions and EquationsMedium
A drone pilot is planning a flight path. The altitude, A, in meters, of the drone over time, t, in seconds, is modeled by the function A(t) = -t^2 + 10t + 20. The pilot needs to know when the drone will be at an altitude of 36 meters. Which equation should the pilot solve?
- A-t^2 + 10t + 20 = 0
- Bt = -36^2 + 10(36) + 20
- C-t^2 + 10t + 20 = 36
- D36t = -t^2 + 10t + 20
Show answer & explanationAnswer & explanation
Correct answer: C. -t^2 + 10t + 20 = 36
The function A(t) represents the altitude of the drone. If the pilot wants to know when the drone is at an altitude of 36 meters, they need to set the function A(t) equal to 36. This results in the equation -t^2 + 10t + 20 = 36.
Why the other options are wrong
- A. This equation would be used to find when the drone is at ground level (altitude 0), not 36 meters.
- B. This equation incorrectly substitutes the target altitude (36) for the time variable (t), which would calculate the altitude at 36 seconds, not the time at 36 meters.
- D. This equation incorrectly multiplies the target altitude by time, which does not represent the given scenario.
Setting Up Quadratic Equations from Word Problems
Translating a real-world problem into a quadratic equation by identifying the unknown, known values, and the relationship that forms a second-degree polynomial.
- Identify the variable.
- Formulate expressions for quantities.
- Set up equation based on given conditions.
- Resulting equation will have x^2 term.
Memory trick: Identify, Relate, Equate: Find what's unknown, how it connects, then set it equal!