Math Quiz that became a Test - Algebra 2

I just gave a 14 question quiz on graphing parabolas and factoring.  It was mostly multiple choice. 

How can I help these students to be able to attack "novel" math problems without saying "I don 't know how to do this?"

Things that caused student distress:

1. Quiz used fractional rather than whole number coefficients on quadratic equation
2. Quiz didn't have constant added to squared portion of quadratic equation - "What do I do when there isn't a plus one?"
3. "How do I find the middle number we used on the table of values?" aka how do I find the x value for the vertex
4. "What do I do with the x value I just found?" when the student needed to plug the value back into the original equation.
5. "How do I decide if the parabola opens up or down?"
6. "Do I change the sign or don't I?" when given a quadratic in vertex form, usually referring to changing sign of h, but not of the k value.
7. "Do I change the sign or don't I?" when given a quadratic in intercept form and they needed to find the x value of the vertex.
8. "What is a solution of the equation? How do I do that?" when given a quadratic equation that isn't solved for zero.
9. "Aren't both of these answers correct?" when looking at solutions of a quadratic equation that had two positive or two negative values; thinking that the multiplication of them would give positive so it wouldn't make a difference?
10. "How do you factor x^2+20x-96=0? There aren't any factors of -96 that add up to 20." when all that was written down was 2 and -48 for factors; needed to list more factors to find the correct ones.

I have had students check their homework with videos I have done outlining what to do to solve and why.  What ideas would be helpful to help them generalize what they know to a new, similar problem?