GED Mathematical Reasoning TestAlgebraic Problem Solving with Expressions and EquationsMedium
A meteorologist is tracking the temperature in a city. The temperature (T) in degrees Celsius over a 24-hour period can be modeled by the function T(h) = -0.5h^2 + 12h - 50, where 'h' is the hour of the day (0 ≤ h ≤ 24). At what hour of the day does the maximum temperature occur?
- A10 am (h=10)
- B12 pm (h=12)
- C8 am (h=8)
- D14 pm (h=14)
Show answer & explanationAnswer & explanation
Correct answer: B. 12 pm (h=12)
The temperature function is a quadratic equation, representing a parabola opening downwards. The maximum temperature occurs at the x-coordinate (in this case, 'h') of the vertex of the parabola.
Why the other options are wrong
- A. This is an incorrect calculation for the vertex 'h' value.
- C. This is an incorrect calculation for the vertex 'h' value.
- D. This is an incorrect calculation for the vertex 'h' value.
Quadratic Vertex (Time of Max/Min)
For a quadratic function f(x) = ax^2 + bx + c, the x-coordinate of the vertex, given by x = -b / (2a), represents the input value (often time) at which the function reaches its maximum or minimum output.
- If 'a' is negative, the vertex is a maximum.
- If 'a' is positive, the vertex is a minimum.
- The formula x = -b / (2a) is crucial for finding the time/input of the extremum.
Memory trick: Vertex Time Varies, Value Varies.