Homework 3

Let $M\subset \mathbb{R}^3$ be the image of the map $\varphi: \mathbb{R} \longrightarrow \mathbb{R}^3$ where $\varphi(t) = (t^2,t^3,t^4)$.  Prove that $M$ is an affine variety and give a basis for the vanishing ideal $I(M)$.