$T\phantom{\rule{mediummathspace}{0ex}}:\phantom{\rule{mediummathspace}{0ex}}R2\left(x\right)\phantom{\rule{mediummathspace}{0ex}}->R2\left(x\right)\phantom{\rule{mediummathspace}{0ex}}defined\phantom{\rule{mediummathspace}{0ex}}by\phantom{\rule{mediummathspace}{0ex}}T(a{x}^{2}+bx+c)=2ax+b$