First of all we need to what the graph of x^2 looks like, because x^2 is in the same form as x^2+bx+c, where b=0, and c=0, and a=1

so:
-putting a positive whole number in for "a" we see that the graph has been pushed together
-putting a fraction in for "a" we see that the graph has been streched
-putting a negative number in for "a" we see that the graph has been turnned upside down
-putting a negative fraction in for "a" we see that the graph has been turnned upside down, and expanded
-putting a negative whole number in for "a" we see that the graph has been turnned upside down, and pushed together

so:
-putting positive number in for "b" moves the vertex of a graph along the line x+c where "c" is the same as in the "c" in your original equation
-putting negative number in for "b" moves the vertex of a graph along the line -x+c where "c" is the same as in the "c" in your original equation

so:
-putting a negative number in for "c" moves the vertex of the graph down "c" units
-putting a positive number in for "c" moves the vertex of the graph up "c" units