For real numbers x, let
f(x) = x + 2 if x > 3,
f(x) = 2x^2 + 3x + a if x <= 3.
What must the value of a be to make the piecewise function continuous (which means that its graph can be drawn without lifting your pencil from the paper)?
The two expressions must be equal when x = 3, so:
3 + 2 = 2*3^2 + 3*3 + a
5 = 27 + a
I'll leave you to find a from this.