Question

Which numbers are roots of the polynomial function shown? Check all that apply. –4 –2 0 2 4 6 On a coordinate plane, a graph shows a wave with a minimum value of negative 1 and a maximum value of 1.75. The wave crosses the x-axis at (negative 4, 0), crosses the y-axis at (0, 1), and crosses the x-axis again at (2, 0) and (6, 0).

Answer 1

Answer:

roots at  -4, 2, 6

Step-by-step explanation:

This appears to be a cubic polynomial since it has a local maximum and a minimum...  Also there are 3 roots.

f(x) = a*(x + 4)*(x - 2)*(x - 6)

with f(0) = 1  =  a*(4)*(-2)*(-6)

1 = a * 48

a = (1/48)

f(x) = (1/48)*(x + 4)*(x - 2)*(x - 6)

f '(x)  = (1/48) (x  - 2)(x - 6) + (1/48)*(x  + 4) [  (x - 6) + (x - 2) ]

f '(x)  = (1/48) (x  - 2)(x - 6) + (1/48)*(x  + 4) [ 2x - 8 ]

...

f(x) = (1/48)*(x + 4)*(x - 2)*(x - 6)

roots at  -4, 2, 6