GED Mathematical Reasoning TestAlgebraic Problem Solving with Expressions and EquationsMedium
A meteorologist is tracking the temperature (T) in degrees Celsius over a 24-hour period, modeled by the function T(h) = -0.05h^2 + 1.2h + 5, where 'h' is the hour of the day (0 ≤ h ≤ 24). At what hour of the day does the maximum temperature occur?
- A12 hours
- B10 hours
- C8 hours
- D14 hours
Show answer & explanationAnswer & explanation
Correct answer: A. 12 hours
Since the leading coefficient (-0.05) is negative, the parabola opens downwards, indicating a maximum temperature. The hour at which the maximum temperature occurs is the x-coordinate (h-coordinate) of the vertex. Use the formula h = -b/(2a) = -1.2/(2*(-0.05)) = -1.2/(-0.1) = 12. So, the maximum temperature occurs at 12 hours.
Why the other options are wrong
- B. This is an incorrect calculation; it might be half of 20, but the correct calculation is 12.
- C. This is an incorrect calculation for the vertex's x-coordinate.
- D. This is an incorrect calculation for the vertex's x-coordinate.
Quadratic Vertex (Time of Max/Min)
The x-coordinate of the vertex of a quadratic function represents the input value (often time) at which the function reaches its maximum or minimum output.
- For f(x) = ax^2 + bx + c, the x-coordinate of the vertex is -b/(2a).
- If 'a' is negative, this x-coordinate gives the time of maximum.
- If 'a' is positive, this x-coordinate gives the time of minimum.
Memory trick: Optimal Input: Just find the x of the vertex!