Praxis Core Academic Skills for Educators: Mathematics (5733)Algebra and FunctionsMedium
A scientist is conducting an experiment where the temperature, T(h), in degrees Celsius, of a substance changes according to the function T(h) = (h - 4)^2 + 10, where h is the number of hours since the experiment began. What is the minimum temperature reached during the experiment?
- A14°C
- B4°C
- C16°C
- D10°C
Show answer & explanationAnswer & explanation
Correct answer: D. 10°C
The function T(h) = (h - 4)^2 + 10 is in vertex form, y = a(x - h)^2 + k. For a parabola opening upwards (since a=1 > 0), the minimum value (vertex) occurs at (h, k). In this function, the vertex is at (4, 10). The minimum temperature is the y-coordinate of the vertex, which is 10°C.
Why the other options are wrong
- A. This might be a result of adding 4 and 10, or evaluating at h=0: T(0) = (-4)^2 + 10 = 16 + 10 = 26.
- B. This is the time (h-coordinate) at which the minimum temperature occurs, not the minimum temperature itself.
- C. This is 4^2, perhaps from confusing the h-value with the k-value.
Vertex Form of a Quadratic Function
The vertex form of a quadratic function is y = a(x - h)^2 + k, where (h, k) are the coordinates of the vertex. If a > 0, the parabola opens upwards and (h, k) is the minimum point. If a < 0, it opens downwards and (h, k) is the maximum point.
- Immediately reveals the vertex (h, k).
- h is the x-coordinate of the vertex (axis of symmetry).
- k is the y-coordinate of the vertex (minimum or maximum value).
Memory trick: Vertex is (H, K), just like a King's Home!