Final answer:
The initial temperature and the maximum temperature of the component are both 144°F, the temperature never falls below zero degrees, and it does not increase for the entire duration of the test. Due to the ambiguity of one statement, it can't be assessed as true or false.
Step-by-step explanation:
The quadratic function missing in the question appears to be of form t² - 24t + 144 for t = 0 to t = 30. This function models the temperature changes of a component over time during the experiment. To answer the statements given by the student, let's analyze the function step by step:
- The coefficient of the t² term is negative, which indicates the temperature function opens downward, meaning the temperature will reach a maximum at some point.
- The initial temperature of the component is given by the function's value at t=0. Plugging in 0 gives 0² - 24(0) + 144 = 144°F.
- The vertex of this parabola represents the maximum temperature; since the axis of symmetry is t=-b/2a, here t=24/2=-12, but this value is out of our range 0 to 30. So, the maximum within [0,30] is at one of the endpoints. Function values at t=0 and t=30 are 144, which matches the maximum temperature statement.
- Since the graph of the temperature function is a downward-opening parabola, the temperature is initially increasing and then decreasing. It is not increasing for the entire duration of the test.
- The component will have the same temperature at t and t = 24, if t=12, because 12 is the axis of symmetry. However, this statement is written incorrectly, preventing clear analysis.
- As we found that the temperature is 144°F at t=0 and t=30, and because our parabola opens downward (indicating a peak in between), 144°F is indeed the maximum temperature reached during the experiment within the given range.
- Given that the quadratic function never results in a negative number within the interval, the temperature of the component is never less than zero degrees.
In summary, the initial temperature of the component is 144°F, the maximum temperature reached by the component during the experiment is 144°F, and the temperature of the component is never less than zero degrees. The temperature is not increasing for the duration of the test since it's a quadratic function that models a rise and then a fall in temperature. We can't definitively answer the fourth statement due to an ambiguous mention of t and t=24.