For this quiz, I do not allow calculators. The questions are primarily conceptual, and the minimal arithmetic that's required should not be a problem for algebra students.
With that said, I get everyone started as quickly as I can with the understanding that they may use the entire class period for the quiz.
I will grade this quiz (solution key provided) in a way that allows for partial credit on every problem. For instance, problem 3 is worth 5 points: 1 point for each root, 1 for the y-intercept, 1 for the end behavior. Similarly, the synthetic substitution problems are worth 4 points each: 2 points for understanding the method, 2 points for carrying it out correctly. For number 6, students could earn 2 points for finding the correct quadratic factor and another 2 points for finding the correct roots.
Taking a similar approach to the rest of the problems, I wound up with a total of 34 points possible. The precise number doesn't really matter; what's important is that I strike a balance between assessing conceptual mastery and computational accuracy. Both are important, and one should not completely outweigh the other. (MP 6)