How to linearly interpolate two functions?

[glass remnant]

I'm watching this video to better understand shaders https://youtu.be/60VoL-F-jIQ?t=211. He is linearly interpolating 2 equations. I don't understand how he arrived at the conclusion that a(1-x) + bx is the linear interpolation of a = x^2 and b = 1 - (x - 1)^2. I've been searching for a while for keywords on linear interpolation, but all I find is how to linearly interpolate values and not equations. How did he do that?
TL;DR: How did he arrived at equation 3 from equations 1 and 2

1. a = x^2
2. b = 1 - (x - 1)^2
3. a(1-x) + bx