A Study of the Top MBA Programs Attempted to Predict $y =$

A study of the top MBA programs attempted to predict $y =$ the average starting salary (in $\$ 1000$ 's) of graduates of the program based on $x =$ the amount of tuition (in $\$ 1000$ 's) charged by the program. After first considering a simple linear model, it was decided that a quadratic model should be proposed. Which of the following models proposes a 2nd-order quadratic relationship between $x$ and $y$ ?

A) $E ( y ) = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 1 } x _ { 2 }$
B) $E ( y ) = \beta _ { 0 } + \beta _ { 1 } { } ^ { x } 1$
C) $E ( y ) = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 1 } ^ { 2 }$
D) $E ( y ) = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 1 } ^ { 2 } + \beta _ { 3 } x _ { 1 } ^ { 3 }$