The i7-2670QM CPU includes a baked in
HD 3000 graphics processor which isn't compatible with W10, according to Intel's latest table:
http://www.intel.com/content/www/us/en/support/graphics-drivers/000005526.html (though you
might be able to run it under a Compatibility mode).
The latest W10 (both Catalyst and Crimson) x64 drivers for the HD69xxM series GPU are here:
http://support.amd.com/en-us/download/desktop/legacy?product=legacy3&os=Windows+10+-+64 (read the blurb carefully, I'd opt for the Catalyst, they were released for W10 Release day, and they should take up
much less drive space once installed, turn off Windows
driver updates or they'll soon revert to the 'bad' drivers).
I think the issue is really down to the 'switchable' graphics (simplified: on the original OS by default, it would boot from the HD 3000, only switching to the AMD/ATI when on mains power and extra capabilities were needed for certain programs and tasks), which you should be able to change in the BIOS - but probably only to on (switchable, boots on Intel, can switch to and from AMD within Windows when required), or off (Intel only). Because this is hardware/BIOS driven, I don't think the full switchable graphics are possible or supported on W10.
I might be wrong, it would probably take some searching on specialist fora to be sure whether they can be made to work as they used to/should or not, on W10. I haven't had recent access to a notebook of this type, so this is theory only.
The best you could hope for in the event that your system isn't fully supported in w10 is that the BIOS can enable the AMD/ATI GPU
only, this would give you better graphics power, should enable the installation of the latest drivers (above) but with the main drawbacks of extra heat being produced and a much lower run time on battery power.
There's a slim chance that disabling the Intel graphics component from within the Device Manager > Display adapters section would force the switch to the AMD - but, as that's set in the BIOS, I'm not at all hopeful - and recovering from the failure of Windows not finding *any* display adapter would require a working System Restore point, at least. Not really recommended.