Thanks! :D

f(2)   =   2(2)²- 3   =   5

 

The first part of the function ends at the point  (2,5) .  So the second part of the function must go right up to that point. The line  f(x)  =  ax + 4  would pass through  (2, 5)  if  x  had no restrictions. So...

 

a(2) + 4  =  5

 

2a  =  1

 

a  =  1/2

 

Here's a graph:  https://www.desmos.com/calculator/wdefhkmmdz