Question

Two new store locations of a shoe company have an opening day promotion by offering a discount of x dollars for a particular shoe. The two functions, f(x) = -5x^2 + 168x + 432 and g(x) = -8x^2 + 285x + 108, represent the amount each store earns. Which function, P(x), represents the total amount earned by both new stores?

Answer 1

To find the total amount earned by both stores, you combine the functions f(x) and g(x) by adding them together. The resulting function P(x), which represents the total amount earned, is P(x) = -13x^2 + 453x + 540.

Step-by-step explanation:

The total amount earned by both new stores is represented by combining the two functions. This is done using addition:

P(x) = f(x) + g(x)

P(x) = (-5x^2 + 168x + 432) + (-8x^2 + 285x + 108)

To find P(x), we add the corresponding terms:

P(x) = (-5x^2 - 8x^2) + (168x + 285x) + (432 + 108)

P(x) = -13x^2 + 453x + 540

Therefore, the function that represents the total amount earned by both stores, P(x), is:

P(x) = -13x^2 + 453x + 540