GED Mathematical Reasoning TestAlgebraic Problem Solving with Expressions and EquationsHard
A drone pilot is planning a flight path. The altitude, A, in meters, of the drone over time 't', in minutes, is given by the function A(t) = -t^2 + 10t + 20. When will the drone reach an altitude of 45 meters?
- A5 minutes only
- B4 minutes and 6 minutes
- C3 minutes and 7 minutes
- D2 minutes and 8 minutes
Show answer & explanationAnswer & explanation
Correct answer: A. 5 minutes only
Set A(t) = 45: -t^2 + 10t + 20 = 45. Rearrange into standard quadratic form: -t^2 + 10t - 25 = 0. Multiply by -1: t^2 - 10t + 25 = 0. This is a perfect square trinomial: (t - 5)^2 = 0. So, t - 5 = 0, which means t = 5. The drone reaches 45 meters at only one time, 5 minutes, which is its maximum altitude.
Why the other options are wrong
- B. These values are incorrect; they do not satisfy the equation.
- C. These values are incorrect; they do not satisfy the equation.
- D. These values are incorrect; they do not satisfy the equation.
Solving Quadratic Equations (Applications)
Applying methods to solve quadratic equations (factoring, quadratic formula, completing the square) to real-world problems, often to find specific input values that yield a given output.
- Set the quadratic function equal to the target value.
- Rearrange the equation into standard form: ax^2 + bx + c = 0.
- Choose an appropriate method to solve for the variable (e.g., time, quantity).
- Interpret the solutions in the context of the problem (e.g., positive time, realistic quantity).
Memory trick: Quadratic App: Set it, standard it, solve it!