Plot of Arrhenius Equation with temperature
I believe that this should have been the graph...(please omit the
  negative side of x axis), so concave downwards. Why is there a
  discrepancy?


Your analysis and your graph are correct.  Let's examine why the discrepancy arises.  I've drawn two graphs below.  The top one is similar to your graph, only I'm examining a smaller range on the x-axis.  My lower graph examines an even smaller range and it is a range close to x=0.  You can see that this lower graph appears to be "concave-up" just like the Wikipedia graph you referenced.



Here's a third graph where I changed the numerator from -1 to -100, notice how it moves the curve further to the right along the x-axis.  



Depending upon 1) what numbers we put in the numerator and denominator of our exponential equation and 2) depending upon how we scale our axes, we can dramatically change how our graph appears.  There will always be a relatively flat part to this curve located close to x=0, then there will be a concave-up section, followed by a concave-down section, and finally another relatively flat section further out on the x-axis.  You happened to choose a large range (up to x=60-70) for the x-axis of your graph.  This compressed your graph, so it did not show the first two parts of the curve (the relatively flat part located close to x=0 and the concave-up section) clearly.