Y=ax^2 + bx+c

y=a (x+3) (x+9) (x+20)

Are these quartic or quadratic and why?

The degree of a polynom is given by the highest power of x.

For second degree (quadratic) we have x²: so ax²+bx+c is quadratic

For quartic: we would have x⁴. None of them quartic.

For y=a (x+3) (x+9) (x+20), by expanding we get an x³. So this is cubic, or of third degree.