You can get the following Asus X550ZA-WB11 for $450. It has a quad core AMD A10-7400p APU it's processing performance would be about equal to an Intel Core i3 CPU. The integrated Radeon R6 (Kaveri) is more powerful than Intel's mainstream HD 5500 graphics core. But less powerful an Intel HD Iris Pro graphics core which are only in laptops that are double your budget. The A10 APU consumes more power than Intel CPUs so battery life would generally not be as good as a laptop with an Intel CPU.
http/www.newegg.com/Product/Product.aspx?Item=N82E16834232500&cm_re=a10-7400p-_-34-232-500-_-Product
If possible, I recommend you bump up your budget to $570 so that you can buy the ASUS Laptop X555LB-NS51 which has a Core i5-5200u, nVidia 940m graphics chip and a 1080p screen. All mobile core i5 CPUs are dual core CPUs, but it is more powerful than the A10-7400p. The nVidia 940m is far more powerful than the Radeon R6 (Kaveri) graphics core and it should allow you to play all Source Engine games at 1080p with high settings since the Source Engine is not that demanding. However, it is not good enough to play most modern games at 1080p.
http/www.newegg.com/Product/Product.aspx?Item=N82E16834232376
Click link below for benchmarks.
http
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