Question

Without plotting any points other than intercepts, draw a possible graph of the following polynomial:
f(x) = (x + 8)3(x + 6)2(x + 2)(x – 1)3(x – 3)4(x – 6).

Answer 1

you got the zeros right? aka the x intercepts?

Answer 2

yeah, aren't they (x =-8), (x=-6), (x=-2), (x=1), (x=3), and (x=6) ?

Answer 3

ok good

Answer 4

then look at the exponents

Answer 5

if they are odd, the graph crosses at that point on the x axis
if they are even the graph touches there but does not cross
for example at \(x=-8\) the factor is \((x+8)^{\color{red}3}\) and since \(\color{red}3\) is odd, it crosses the x axis at \(-8\)

Answer 6

hmm ok

Answer 7

what is the degree of the whole thing?

Answer 8

4?

Answer 9

oh heck no

Answer 10

add up all the exponents

Answer 11

the exponents of each factor that is , include the 1's

Answer 12

oh whoops :/ so 14

Answer 13

yeah even number so it tells you it starts upper left and ends upper right

Answer 14

here is a nice picture
http://www.wolframalpha.com/input/?i=%28x+%2B+8%29^3%28x+%2B+6%29^2%28x+%2B+2%29%28x+%E2%80%93+1%29^3%28x+%E2%80%93+3%29^4%28x+%E2%80%93+6%29+domain+-9..7

Answer 15

ok :) does it matter how much the line drops in between each x intercept, or as long as it meets the line where it's supposed to and how its supposed to?