`a_0 = 3, a_2 = 0, a_6 = 36` 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 = 3 => f(0) = a*0^2 + b*0 + c => c = 3`

`a_2 = 0 => f(2) = a*2^2 + b*2 + c => 4a + 2b + c = 0`

`a_6 = 36 => f(6) = a*6^2 + b*6 + c => 36a + 6b + c = 36`

You need to replace 3 for c in the next two equations, such that:

`4a + 2b + 3 = 0 => 4a + 2b = -3`

`36a + 6b + 3 = 36 => 36a + 6b = 33 => 18a + 2b = 11`

Subtract the equation `4a + 2b = -3` from the equation `18a + 2b = 11` :

`18a + 2b - 4a - 2b = 11 + 3`

`14a = 14 => a = 1`

Replace 1 for a in equation `4a + 2b = -3` , such that:

`4 + 2b = -3 => 2b = -7 => b = -7/2`

Hence, the quadratic model for the given sequence is `a_n = n^2 - (7/2)*n + 3.`