Question

Construct a polynomial function that might have the given graph Which of the following is a polynomial function that might have the given graph? ОА. (x) = - x+2yx + 1)(х - 1) Ос. Қя) = (x+2yx + 12(x-1) ОЕ. Қя) = (х + 2ух + 11х - 112 ов. (x) = (х +27 x + 1)(х – 12 ор. (x) = (х + 27х + 12(x-1) Оғ. (x) = (х + 24х + 1х - 1)

Answer 1

if a polynomial function crosses x axis at a x=c , then polynomial function will have a term (x-c).

if a polynomial function just touches x axis at x=k , then polynomial function will have term (x-k)²

given graph crosses x axis at x=-2 . so it will have term (x+2).

given function just touches x axis at x= -1 . so it will have term (x+1)².

given graph crosses x axis at x=1 . so it will have term (x-1).

so

function can be represented using this terms as

f(x) =C *(x+2)(x+1)²(x-1)'

here C is any constant .

from graph , it passes through (0,-1) . so apply this to equation and find C (when x=0 , f(x) is -1)

f(0)= -1= C*(0+2)(0+1)²(0-1)

-1= C*-2

TA

so equation is

f(x) = (x + 2)(x+1)?(x – 1)

option D