`a_0 = -3, a_2 = -5, a_6 = -57` 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 = -5 => f(2) = a*2^2 + b*2 + c => 4a + 2b + c = -5`

`a_6 = -57 => f(6) = a*6^2 + b*6 + c => 36a + 6b + c = -57`

You need to replace -3 for c in equation `4a + 2b + c = -5` :

`4a + 2b - 3 = -5 => 4a + 2b = -2 => 2a + b = -1`

You need to replace -3 for c in equation `36a + 6b + c = -57` :

`36a + 6b - 3 = -57 => 36a + 6b = -54 => 6a + b = -9`

Subtract `2a + b = -1` from `6a + b = -9` , such that:

`6a + b - 2a - b= -9 + 1`

`4a = -8 => a = -2`

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

`2*(-2) + b = -1=>-4 + b = -1 => b = 3`

Hence, the quadratic model for the given sequence is `a_n = -2n^2 + 3n - 3.`