Question

For the graph attached inside, what is the minimum possible degree of the polynomial?

And is the leading coefficient of the polynomial positive or negative?

**I'm not sure how to find the min. degree :/ but would it be positive? since the graph starts above 0?

Answer 1

graph :)

Answer 2

how many times does the graph change direction?

Answer 3

4?

Answer 4

in other words, how many local mins or local maxes are there?

Answer 5

so four mins and maxes then?

Answer 6

a local min is where the graph bottoms out (goes down then comes back up)

a local max is where the graph peaks (goes up then comes back down)

Answer 7

ohh so 2 local mins and 1 local max?

Answer 8

here's one visual

http://01.edu-cdn.com/files/static/mcgrawhill-images/9780071393089/f0086-02.jpg

Answer 9

good, so 2+1 = 3 turning points total

Answer 10

the min degree is equal to the number of turning points + 1

min degree = (number of turning points) + 1

min degree = 3 + 1

min degree = 4

Answer 11

ohh okay awesome! :)

Answer 12

so for the coefficient part.. would that be based off of where the graph begins? :/

Answer 13

think of a parabola

if it opens upwards, then is the leading coefficient positive or negative?

Answer 14

it would be positive ?

Answer 15

yes it would be

Answer 16

the same applies to any even degree polynomial

Answer 17

okay:) so in this case, it's opening upwards right? so it'd be positive too? :)

Answer 18

yep, it opens upwards which means it has a positive leading coefficient

Answer 19

okie :) yay! thanks a bunch!!

Answer 20

yw

Answer 21

okie :) yay! thanks a bunch!!