Three Times the Perfect Stride

A model is trained on the loss

$L(w) = 4w^2 - 24w + 41$

with the usual update rule

$w \leftarrow w - \alpha\, L'(w)$

starting from $w_0 = 8$.

For this loss there is exactly one learning rate $\alpha^{\star}$ that would carry the parameter from $w_0$ onto the minimising value of $w$ in a single step — a perfect stride, landing precisely at the bottom.

An impatient engineer decides that if $\alpha^{\star}$ is good, then training three times faster must be better, and runs the model with

$\alpha = 3\,\alpha^{\star}$

Starting again from $w_0 = 8$, what is the value of the loss after one step at this larger learning rate?

Give the loss rounded to 2 decimal places.