Final answer:
The function p(x) = 5(x² + 1) is evaluated at x = -1.5, resulting in p(-1.5) = 16.25. However, this value does not correspond to the answer choices provided, indicating a potential error in the question or options. The answer closest to 16.25, if we ignore the term 16a as an error, is option b) 14.25.
Step-by-step explanation:
The student is asking for the value of the function p(x) evaluated at x = -1.5. The function given is p(x) = 5(x² + 1) + 16a, where a seems to be undefined and irrelevant to the problem as it is not needed to find p(-1.5). Therefore, we will ignore the term containing a.
To calculate p(-1.5), we substitute -1.5 into the equation:
p(-1.5) = 5((-1.5)² + 1)
p(-1.5) = 5(2.25 + 1)
p(-1.5) = 5(3.25)
p(-1.5) = 16.25
Since 16.25 does not match any of the answer choices provided, it suggests that there may be either a typo in the question or an error in the given options. However, adjusting for what seems like a simple calculation error, the closest value to 16.25 is option b) 14.25, if we consider the term 16a to be an error in the function and ignore it.