Question

find x intercpts of the polynomial function state wether the graph crosses the x axis or touches and turns around at each intercept f(x)=4x^2-x^3

Answer 1

intercepts are x=0,4 I forget the rule how we know wether it crosses or turns around??

Answer 2

by the degree

Answer 3

i think it is related to "multiplicity" of a zero

Answer 4

yes that's what I meant if it is odd it crosses but if its even it touches but turns around

Answer 5

thats how the graph looks..
at x = 0, it is just touching x axis and turning around
at x=4, it is actually crossing the x ais

Answer 6

thanks

Answer 7

f(x)=4x^2-x^3 = x^2(4-x)

Notice that the multiplicity of root "0" is 2 here, i think this is the reason it turns around..

Answer 8

I c