Question

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 1

X = 0 ; y = 10 ; 10 = a(0) + b(0) + c
c = 10

x=2 ; y = 15 ; 15 = a(4) + b(2) + 10 ; 5 = 4a+2b
x=4 ; y=18 ; 18 = a(16) + b(4) + 10 ; 8 = 16a + 4b 

2(5) = (4a+2b)2
-
    8 = 16a + 4b
    2 = -8a

a = -0.25

b = 2

y = (1/4)x^2 + 2x + 10 ; 4y = x^2 + 8x + 40

Answer 2

Answer:

-1/4 x^2 +3x+10

Step-by-step explanation: