Question

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i need help please with this graph finding the roots from algebra 1
heres the question :The points plotted below are on the graph of a polynomial. How many roots of the polynomial lie between x = -4 and x = 3?

Answer 1

if you draw a curve through the points, you get this M shaped figure

see the attached image

Answer 2

how many times does the red curve either touch the x axis or cross the x axis?

Answer 3

is it 4?

Answer 4

hi

Answer 5

hi

Answer 6

yes 4 times

Answer 7

so there are 4 roots (aka 4 x intercepts)

Answer 8

does it also apply to this question ? which is another problem :The points plotted below are on the graph of a polynomial. Some of the roots to this polynomial are integers. Which of the following x-values are roots of the polynomial? Check all that apply.
A. x = -2
B. x = 0
C. x = 1
D. x = -5
E. x = -4
F. x = -3

Answer 9

yeah you'll follow the same steps. Draw a curve through the points and see where the x intercepts are

Answer 10

instead of listing out how many there are, you list out what the actual roots are

Answer 11

i drawn the line and what should i be looking at because it has the 4 roots like the previous question , or should i be looking at where the each dot of the x-axis are plotted ?

Answer 12

they want you to report where on the number line (the horizontal number line, aka the x axis) the curve crosses

Answer 13

for example, say we had this curve



the curve in my example above goes through -2 on the x axis, so -2 is a root of this function

Answer 14

so its where the dot touches the number so in mine one of them would be -3

Answer 15

-3 is one root, yes

Answer 16

-2 has a dot there but it doesnt touch is that consider a root aswell as 1 on the positive side?

Answer 17

-2 looks like another root

Answer 18

on the positive side i see a 1 but the dot is above and a little to the side of 1 thats is that consider a root ? i only see 3 roots overall but i am not sure if i am right on the 1 ?

Answer 19

yes, 1 looks like a root as well

Answer 20

-3, -2, and 1 look like the three roots

well actually there is a 4th root slightly after x = 1

Answer 21

this is all educated guesswork really

Answer 22

is it 0 ?

Answer 23

0 isn't a root

Answer 24

if theres 4 roots then it will be either -5 or -4 but i dont see how will it have 4 roots if theres no roots close to those two numbers

Answer 25

like I said, if you draw a curve through all the points, this curve looks like it goes through x = -3, x = -2 and x = 1 on the x axis

the fourth root it goes through is some number between 1 and 2 (like 1.3 or something)

Answer 26

because in my answer options it only has 3 roots that i found theres no anser of a 1.3 i know what your reffering too i se the dot between them to but in my options i believe theres only 3 since they arent giving me the 4th one

Answer 27

see attached

Answer 28

that 4th root (the one between x = 1 and x = 2) won't be reported

Answer 29

i seen your graph and yes i agree it doesnt give it to me in the answer options

Answer 30

because the only options i have left is -5 , -4, and 0

Answer 31

It's definitely not -5

Answer 32

not -4 or not 0 either

Answer 33

so i guess it only 3 roots for the problem they gave me

Answer 34

yeah ignore that root between x = 1 and x = 2