Question

f(x)=(x-4)^2(x+5)^2
1)Find Zero's of multiplicity
(I got x=4 with 2 multiplicty and -5 with multiplicity of 2)
2) where on graph touches x-axis (Is it 4)
3) number of turning points
4) end behavior
Can anyone help?

Answer 1

1) zeros are at x=4 and -5 as you said

Answer 2

it touches x-axis at x=4 and x = -5

Answer 3

two minimum turning pints at x=4 and x=-5

Answer 4

Thank you but what would my end behavior be?

Answer 5

as x --> +infinity f(x) --> + infinity
as x---> - infinity f(x) ----> + infinity

Answer 6

there will also be a maximum turning point between x = -5 and x = 4

altogether 3 turinng points