Question

# Homework: 6.2_HW Find the quartic function that is the best fit for the data in the table below. Report the model with three signifi X -2 -1 0 1 2 3 4 Y -2 -1.25 0 -1.25 -2 6.75 40 (Simplify your answer. Do not factor. Use integers or decimals for any numbers in the expression.)

Answer

-0.35416667x^4 - 0.0625x^3 + 0.52083333x^2 - 0.29166667x

- Find the general form of a quartic function: y = ax^4 + bx^3 + cx^2 + dx + e.
- Using the table of values, we can create a system of equations to solve for the coefficients of the quartic function:
- Substitute x and y values from the table to the general formula: -16a -8b -4c -2d + e = -2, -a -b -c -d + e = -1.25, e = 0, a + b + c + d + e = 0, 16a + 8b + 4c + 2d + e = -2, -81a - 27b - 9c - 3d + e = 6.75, 256a + 64b + 16c + 4d + e = 40.
- Solve the system of equations:
- a = -0.35416667, b = -0.0625, c = 0.52083333, d = -0.29166667, e = 0.