At a pottery factory, fuel consumption for heating the kilns varies with the size of the order being fired. In the past, the company recorded the figures in the table.

$($a$)$ Find an equation of the form $y=a{x}^2+bx+c$ whose graph contains the three points corresponding to the data in the table. $($b$)$ How many platters should be fired at one time in order to minimize the fuel cost per platter? What is the minimum fuel cost per platter.

$\backslash$table$[[\backslash$table$[[x=$ Number$],[$of Platters$]],\backslash$table$[[y=$ Fuel Cost$],[$per Platter$]]],[4,$$$2\mathrm{.}26$