Question

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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.

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.

x 0 2 4 6 8 10
f(x) 10 15 18 19 18 15

f(x)=ax^2+bx+c

Answer 1

It appears that you are trying to find a quadratic function in standard form that models the number of guests at the large resort as a function of the number of months since the beginning of the year.

To do this, you can use the given data points to solve for the constants a, b, and c in the standard form of the quadratic function f(x) = ax^2 + bx + c.

To find the values of a, b, and c, you will need to have at least three data points. You can then use these data points to solve a system of three equations with three variables.

For example, using the data points (0, 10), (2, 15), and (4, 18), you can set up the following system of equations:

f(0) = 10 = a(0)^2 + b(0) + c

f(2) = 15 = a(2)^2 + b(2) + c

f(4) = 18 = a(4)^2 + b(4) + c

Solving this system of equations will give you the values of a, b, and c that you can use to write the standard form of the quadratic function that models the data.

I hope this helps! Let me know if you have any questions or need further assistance.

Explanation: