Quadratic functions, parabolas

ƒ(x) = ax2 + bx + c
   y = ax2 + bx + c

   a    "direction"
(up or down?) 		   b       c       vertex      extremum  
(min or max?) 		   range        x-intercepts    y-intercept #solutions
quadratic EQ
x2
-x2
x2 + 1
x2 - 1
-x2 + 1
-x2 - 1
x2 + x
x2 - x
-x2 + x
-x2 - x
x2 + x + 1
x2 + x - 1
x2 - x + 1
x2 - x - 1
-x2 + x + 1
-x2 + x - 1
-x2 - x + 1
-x2 - x - 1

Hint: every row is different. No graphs are the same.

What is the relationship between a and the "direction" of the graph?
What is the relationship between which extremum and the "direction" of the graph?
What is the relationship between c and the y-intercept?
What is the relationship between the number of x-intercepts and the number of solutions?