The effect of reversing the sign of b on the graph of f(x) = ax^2 + bx + c is that the graph is reflected about the y-axis.
Or the value for f(x) is equal to the value obtained if -x was used instead of +x.
This is evident from the fact that :
a(-x)^2 - b(-x) + c = ax^2 + bx + c
You can present this to an audience by using the help of an online graphing tool. Take the graphs of ax^2 - bx + c and f(x) = ax^2 - bx + c on the same figure and use it in your presentation to show accurately that the points x which earlier gave the value for f(x) are now replaced by -x.
Changing the sign of b in the function f(x) = ax^2 + bx + c reflects the graph about the y-axis.