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.

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

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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.

Step-by-step explanation:

arrange the equations with like terms in columns.

analyze the coefficients of x or y.

add the equations and solve for the remaining variable.

substitute the value into either equation and solve.

check the solution.

step-by-step explanation: