Final answer:
To determine a quadratic function to model the total number of bricks in the stack, we can use the formula for the sum of an arithmetic series with a common difference of -1.
Step-by-step explanation:
To determine a quadratic function to model the total number of bricks in the stack, we need to understand the pattern between the number of rows and the total number of bricks. Let's say the number of rows is denoted by x and the total number of bricks is denoted by f(x).
In a stack of bricks, each row will have one less brick than the row above it. So, if the first row has x bricks, the second row will have x-1 bricks, the third row will have x-2 bricks, and so on. We can sum up the number of bricks in each row to get the total number of bricks:
f(x) = x + (x-1) + (x-2) + ... + 1
This is an arithmetic series with a common difference of -1. Using the formula for the sum of an arithmetic series, which is S = (n/2)(a + l), where S is the sum of the series, n is the number of terms, a is the first term, and l is the last term, we can simplify the equation to:
f(x) = (x/2)(x + 1)
So, the quadratic function to model the total number of bricks in the stack is f(x) = (x/2)(x + 1).