Praxis Core Academic Skills for Educators: Mathematics (5733)Algebra and FunctionsMedium
A project manager is analyzing task completion times. The time T (in hours) to complete a certain task is modeled by the function T(n) = n^2 - 6n + 10, where n is the number of resources assigned to the task. What is the minimum time required to complete the task?
- A1 hour
- B10 hours
- C3 hours
- D2 hours
Show answer & explanationAnswer & explanation
Correct answer: A. 1 hour
The function for task completion time is a quadratic equation, T(n) = an^2 + bn + c. Since the leading coefficient 'a' is positive (1 > 0), the parabola opens upwards, and its vertex represents the minimum value of the function.
Why the other options are wrong
- B. This is the y-intercept, T(0) = 10, representing the time with zero resources, which is not the minimum.
- C. This is the number of resources (n) that minimizes the time, not the minimum time itself.
- D. This might be a miscalculation after finding n=3, or an incorrect application of the vertex formula.
Minimum of Quadratic Function
For a quadratic function f(x) = ax^2 + bx + c with a > 0, the minimum value occurs at the vertex, whose x-coordinate is -b/(2a).
- Parabola opens upwards (a > 0).
- Vertex coordinates: (-b/2a, f(-b/2a)).
- The y-coordinate of the vertex is the minimum value.
Memory trick: Positive 'A' means a Valley, Vertex is the Lowest Point.