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).

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