For the function f(x)={ax2+1x<2x+ax≥2f(x) = \begin{cases} ax^2 + 1 & x < 2 \\ x + a & x \ge 2 \end{cases}f(x)={ax2+1x+ax<2x≥2, find the value of aaa that makes fff continuous at x=2x=2x=2.
a=13a = \frac{1}{3}a=31
a=1a = 1a=1
a=23a = \frac{2}{3}a=32
a=3a = 3a=3