Corrected value in a quadratic table

High school · ●●○○○ 20 pts

A student plots

y=ax^2+bx+c

(

a\neq 0

) using seven equally spaced

x

-values

x_1<x_2<\cdots<x_7

, where

x_{k+1}-x_k

is constant. The recorded

y

-values are

51, 107, 185, 285, 407, 549, 717

for

x_1,\ldots,x_7

respectively. Exactly one of these

y

-values was calculated incorrectly. Find the correct value of that

y

-value.