SOLUTION: The number of guests per month at a large resort is given in the table below, where f(x) is the number of guests, in hundreds, x months since the beginning of the year. x 0 2 4

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: The number of guests per month at a large resort is given in the table below, where f(x) is the number of guests, in hundreds, x months since the beginning of the year. x 0 2 4       Log On


   

Question 1139329: The number of guests per month at a large resort is given in the table below, where f(x) is the number of guests, in hundreds, x months since the beginning of the year.
x 0 2 4 6 8 10
f(x) 10 15 18 19 18 15
Use the data in the table to create the standard form of the function that models this situation, where a, b, and c are constants.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Think about the data given. Quadratic model with vertex (6, 19) and two points being (0, 10) and (12, 10).

y=a%28x-6%29%5E2%2B19
-
a%28x-6%29%5E2=y-19
a=%28y-19%29%2F%28x-6%29%5E2
from here, any non-vertex point can be used for evaluating "a".
Trying (0,10):

a=%2810-19%29%2F%280-6%29%5E2=-9%2F36=-1%2F4

highlight_green%28y=-%281%2F4%29%28x-6%29%5E2%2B19%29
Do the necessary multiplication in order to find b.
Already seen are a=-1%2F4, and c=19.