Chapter 8.1, Problem 35PPE

To determine

To find:The polynomial that models the total number of students at both high schools.

Answer to Problem 35PPE

  $-18x^2+228x+2300$

Explanation of Solution

Given information:The number of students at East High School and the number of students at Central High School over a 10-year period can be modelled by the following polynomials.

East High School: $-11x^2+133x+1200$

Central High School: $-7x^2+95x+1100$

In each polynomial, $x=0$ corresponds to the first year in the 10-year period.

Calculation:

The total number of students at both high schools is given by,

  $\begin{array}{l}(-11x^2+133x+1200)+(-7x^2+95x+1100)\\ =-11x^2+133x+1200-7x^2+95x+1100\\ =(-11x^2-7x^2)+(133x+95x)+(1200+1100)[\text{combining like terms]}\\ =-18x^2+228x+2300\end{array}$

Thus, the total number of students is $-18x^2+228x+2300$ .