Question #bc34e

1 Answer
Jan 17, 2018

Please see below.

Explanation:

.

Since the variable #x# has an even exponent, #x^2# is always positive for all values of #x# from #-oo# to #oo#.

Therefore, in:

#y=ax^2#

what determines the direction in which #y# increases is the sign of #a#.

You can make a table of values as you normally would when you want to graph a function and try increasing values of #x# in the function in each case.

You will see how the sign of #a# decides the direction of increase in #y#.

Below, you can see the graph of #y=3x^2# (here, #a=3#):

graph{3x^2 [-10, 10, -5, 5]}

And here is the graph of #y=-3x^2# (here, #a=-3)#:

graph{-3x^2 [-10, 10, -5, 5]}