A dedicated graphics card is not at all necessary to be able to run
games such as Minecraft since Intel already contains an integrated
graphics core within the processor itself. I ran minecraft years ago
without a GPU, and simply used the integrated graphics card that Intel
provided. A dedicated graphics processing unit is used to be able to
achieve higher frame rates since you dedicate the visual processing
portion of applications to a completely dedicated graphics processing
unit, instead of having all the load on the processor itself.
Here's the inside of one of the Intel processors.
@Weirdfisher
In the end here's a few things you can do which @ItzzAlexx did mention.
Updating your PC or really any application/operating system is always
highly recommended due to security updates and performance improvements.
Also resetting your computer to factory settings helps a ton to get a
fresh start. Often unnecessary files and processes add up in the
background overtime. Cleaning your PC entirely can provide a noticeable
difference. There are also options to disable some windows features such
as some of the animations to give your computer a little bit of a
boost. Also go through and make sure you uninstall any software you do
not need. But if you have the money, perhaps it's time you simply
upgrade your PC.
If you have the money, I would highly recommend getting the
https://www.amazon.com/Dell-15-6-Inch-Quad-Core-i5-6300HQ-Processor/dp/B015PYYDMQ.
It's the computer I currently use and I've had it for over a year now. I
take it everywhere I go and haven't gotten a scratch, nor has it needed
a single repair. The retina 4k display is absolutely astonishing. The
Nivida GeForce 960m card may not be the absolute best, however it's
definitely a very good gpu for a laptop, and I can easily achieve
anywhere between 150-350 fps on minecraft with 12 chunk render distance,
and everything else maxed out, however I usually cap the fps to a
constant value of 150. Great value, portable, fairly light weight,
beautiful, powerful gaming machine. Note I did get a more expensive
version with the intel i7 4k resolution etc. when it was on sale,
however the i5 etc. should fit your needs, since getting a processor
such as an i7 and 4k resolution is really only necessary if you have
additional needs such as developing/visual graphics. For gaming the GPU
is really your main concern.