Find the fourth-degree polynomial function whose graph is shown in the figure.

Question

Find the fourth-degree polynomial function whose graph is shown in the figure.

 

*I need to know the correct answer so i can be able to check my answer, thank you!

y= _____________

Answer 1

The graph has zeros at x = 0, 1, 3, 6.  Hence the basic function is:

 

f(x) = ax(x-1)(x-3)(x-6)

 

where a is a constant.  To find the value of a, plug in the known point, (-1,4):

 

4 = a(-1)(-1-1)(-1-3)(-1-6)

4 = 56a

1/14 = a

 

So the polynomial is:

 

f(x) = (1/14)(x)(x-1)(x-3)(x-6) = (1/14)x⁴ - (5/7)x³ + (17/14)x² - (9/7)x