`a_0 = -3, a_2 = 1, a_4 = 9` 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 = 1 => f(2) = a*2^2 + b*2 + c => 4a + 2b + c =1`

`a_4 = 9 => f(4) = a*4^2 + b*4 + c => 16a + 4b + c = 9`

You need to replace -3 for c in equation `4a + 2b + c =1:`

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

You need to replace -3 for c in equation` 16a + 4b + c = 9` :

`16a + 4b - 3 = 9 => 16a + 4b = 12 => 4a + b = 3`

Subtract `2a + b = 2 ` from `4a + b = 3,` such that:

`4a + b - 2a - b = 3 - 2`

`2a = 1=> a = 1/2`

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

`2*(1/2) + b = 2 => 1 + b = 2 => b = 1`

Hence, the quadratic model for the given sequence is `a_n = (1/2)n^2+ n - 3.`