Final answer:
The question addresses different mathematical concepts including simplification of functions, solving quadratic equations, understanding continuous probability distributions, and finding specific probabilities. Key strategies include using the quadratic formula and normalization of probability functions.
Step-by-step explanation:
The student appears to be asking for help with simplifying and analyzing functions. I see multiple functions mentioned, but it seems that there may be a typo in the original function provided. However, discussing some of the excerpts provided, we can tackle quadratic equations, the concept of probability distributions in a continuous function, and the calculation of certain probabilities.
Quadratic equations like x² + bx + c = 0 can be solved using the quadratic formula, which is x = (-b ± √(b² - 4ac)) / (2a). This knowledge can also be applied to find the solutions to projectile motion problems, where the equation is in the form at² + bt + c = 0, with t being time.
When it comes to probability distributions and particularly a uniform distribution between 0 and k, the probability P(0 < x < k) for a continuous function would be 1, assuming the function is properly normalized.