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Active Prelude to Calculus

Activity 1.5.2.
Open a browser and point it to Desmos. In Desmos, enter q(x) = ax^2 + bx + c; you will be prompted to add sliders for \(a\text{,}\) \(b\text{,}\) and \(c\text{.}\) Do so. Then begin exploring with the sliders and respond to the following questions.
(a)
Describe how changing the value of \(a\) affects the graph of \(q\text{.}\)
(b)
Describe how changing the value of \(b\) affects the graph of \(q\text{.}\)
(c)
Describe how changing the value of \(c\) affects the graph of \(q\text{.}\)
(d)
Which parameter seems to have the simplest effect? Which parameter seems to have the most complicated effect? Why?
(e)
Is it possible to find a formula for a quadratic function that passes through the points \((0,8)\text{,}\) \((1,12)\text{,}\) \((2,12)\text{?}\) If yes, do so; if not, explain why not.