`a_0 = 7, a_1 = 6, a_3 = 10` Find a quadratic model for the sequence with the indicated terms.

You need to remember what a quadratic model is, such that:

`a_n = f(n) = a*n^2 + b*n + c`

The problem provides the following information, such that:

`a_0 = 7 => f(0) = a*0^2 + b*0 + c =>  c = 7`

`a_1 = 6 => f(1) = a*1^2 + b*1 + c => a + b + c =6`

`a_3 = 10 => f(3) = a*3^2 + b*3 + c => 9a + 3b + c = 10`

You need to replace 7 for c in equation `a + b + c = 6` :

`a + b +7 =6=> a + b = -1`

You need to replace 7 for c in equation `9a + 3b + c = 10:`

`9a + 3b +7 = 10=> 9a + 3b = 3 => 3a + b = 1`

Subtract `a + b =-1 ` from `3a + b = 1` , such that:

`3a + b - a - b= 1 + 1`

`2a = 2=> a = 1`

Replace 1 for a in equation `a + b =-1`  such that:

`1+ b = -1 => b = -2`

Hence, the quadratic model for the given sequence is `a_n = n^2 - 2n + 7.`