Mark, How do I go about making sure my key light is "color balanced"? thanks so much!
I bought an 18% gray card. I have my subject hold it out in front, shoot them, then use the white balance eyedropper in post (Lightroom).
In your case, it's not color balance. If you added enough yellow to offset that blue/gray on the bottom, your background would look like urine.
What you are seeing are the natural properties of light falling off, and the transistion between different expsosures within your scene.
You have only one problem, there's not enough light reflecting from your floor to the sensor, your solution is to reflect more light to your sensor.
You can either add more light, or increase the reflectiveness of the surface. Adding more background light is not going to help. In fact, your background lights look like they might be a touch hot for how close she is. Ideally I'd move her further away, which will increase the amount of gray you see on the floor.
Play with your key light. Come in at a sharper angle, from up high, feather some light down onto the floor. That light will bounce back up and become fill. A larger light source on your key would really be helpful....but even then, you'll probably still see some gray.
The tile board is nice because it is a lot more reflective than that vinyl, and it really is the poor mans solution to your problem. I'd rather do that than add another light and buy some huge modifiers....plus you get that nice reflection underneath, which is a bonus. Doing that will free up other lights you might have and allow you to use them as a hair light, or a kicker of some sort.

