Question

For 100 points, can someone find the quadratic equation that models data from the table and explain how to solve this?

Answer 1

Answer:

$\textsf{B)} \quad f(x)=1.2x^2 + 13x + 504.3$

Step-by-step explanation:

To find the quadratic equation in the form y = ax² + bx + c that models the given data, we need to use quadratic regression.

Quadratic regression is a statistical method that models the relationship between a dependent variable (y) and an independent variable (x) using a quadratic equation, allowing for the identification of a curved pattern in the data.

To find a model for the given data, input the data into a quadratic regression tool or statistical calculator.

After entering the data into a statistical calculator we get:

• a = 1.209285714
• b = 12.99857143
• c = 504.2571429

Round the values to one decimal place:

• a = 1.2
• b = 13.0
• c = 504.3

Finally, substitute the values of a, b and c into the quadratic regression formula, f(x) = ax² + bx + c:

$\Large\boxed{\boxed{f(x)=1.2x^2 + 13x + 504.3}}$

Additional Notes

While it is possible to perform quadratic regression manually, the process is too complicated and lengthy to include here.