Let
f(x) = 3x^2 + 2 if x <= 3
f(x) = ax^2 + 2 if x > 3
Find a if the graph of y = f(x) is continuous (which means the graph can be drawn without lifting your pencil from the paper).
If x = 3 then
3(3)^2 + 2 = 29
So we need to have
a(3)^2 + 2 = 29
9a = 27
a = 3
See the graph here : https://www.desmos.com/calculator/srad0t3mxn
