Praxis Core Academic Skills for Educators: Mathematics (5733)Algebra and FunctionsMedium
A meteorologist is tracking the temperature in a city. The temperature T (in degrees Fahrenheit) over a 24-hour period can be modeled by the function T(h) = -0.02(h - 14)^2 + 80, where h is the hour of the day (0 ≤ h ≤ 24). What is the maximum temperature recorded during this period?
- A80 degrees F
- B82 degrees F
- C66 degrees F
- D14 degrees F
Show answer & explanationAnswer & explanation
Correct answer: A. 80 degrees F
The function is in vertex form, T(h) = a(h - k)^2 + m. Since a = -0.02 (which is negative), the parabola opens downwards, and the vertex (k, m) represents the maximum point. The maximum temperature is the y-coordinate of the vertex, which is 80 degrees F.
Why the other options are wrong
- B. Incorrectly added the coefficient 'a' to the maximum temperature.
- C. Incorrectly calculated or misinterpreted the vertex form.
- D. This is the hour at which the maximum temperature occurs (h-coordinate of the vertex).
Vertex of Parabola (Vertex Form)
For a quadratic function in vertex form, f(x) = a(x - h)^2 + k, the vertex is at the point (h, k).
- The 'h' value represents the x-coordinate of the vertex.
- The 'k' value represents the y-coordinate of the vertex, which is the maximum or minimum value of the function.
- If 'a' is negative, 'k' is the maximum; if 'a' is positive, 'k' is the minimum.
Memory trick: Vertex is home, (h, k) is the known.