What effect does the value of the coefficient of x^2 have on the graph?

As the coefficient increases, the graph shrinks.
ex.)
for the graph of x^2, 5 of your data points will be (0,0),(1,1),(2,4),(3,9),(4,16)

when you multiply by a coefficient,
ex.)
for the graph of ax^2, a being a stand in for the coefficient, 5 of your data points will be (0,a×0), (1,a×1), (2,a×4), (3, a×9), (4,a×16)

if your coefficient,a, is equal to 4 your data points become: (0,0),(1,4),(2,8),(3,36),(4,64)

if you graph it out you will notice that your graph rises faster and faster incompariaon to the original.

hope this helps good luck