Light travels at the same speed relative to all frames of reference: you, the quasar other objects moving however fast in whatever direction. They all see the
same speed for the
same beam of light. There is no adding or subtracting or otherwise combining the speeds of the light the source and the observer, like you might think. The speed is the same for all! It goes against everyday "common sense" but "common sense" is plain wrong in this case, or to put it more eloquently: "Common sense is the collection of prejudices acquired by age eighteen" (Albert Einstein).
Light travels the same speed with respect to all frames of reference irrespective of their motion. This is a most revealing observation and shocks people when they comprehend the meaning of this statement for the first time, but that's how nature does it.
