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

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).

in progress 0
Mia 2 weeks 2021-10-03T14:38:14+00:00 1 Answer 0

Answers ( )

    0
    2021-10-03T14:39:58+00:00

    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

Leave an answer

45:7+7-4:2-5:5*4+35:2 =? ( )