Question

Describe the graph of the function f(x) = x3 − 18x2 + 107x − 210

Answer 1

what info do you usually need...

this is a cubic equation, polynomial

Answer 2

remember the look of y=x^3

Answer 3

Describe the graph of the function f(x) = x3 − 18x2 + 107x − 210. Include the y-intercept, x-intercepts, and the shape of the grap

Answer 4

Thats what I need

Answer 5

that is the general shape, the squared term will mess with that middle section a bit


Graph the general form here

y = A*x^3 + B*x^2+C*x+D

Select 'add sliders' for ABCD, mess with those coefficient values and watch the graph

Answer 6

https://www.desmos.com/calculator

Answer 7

well the y intercept is when x=0, just solve that point

Answer 8

I just dont know how to describe it, nor the shape

Answer 9

Maybe start by saying, the general shape is similar to that of y=x^3

did you make that graph with sliders on the other page?

Answer 10

notice if A is + vs A is -, the way the ends of the graph look

Answer 11

Yeah made the graph on the page you sent me

Answer 12

You can show that a cubic has at least one real root (x-intercept), because if you take very large values for x, the cube term dominates, and the ends of the graph for x is large + and -, go off to huge values for f(x) in opposite directions...

the range is then all real numbers, and it must cross the x axis somewhere at least once then, to go from -huge number to a + huge number, the sign must change

Answer 13

Go to that site, in the place where you put things in on the left.. put

a*x^3+b*x^2+c*x+d

hit to add sliders for all 4, a,b,c, and d

play with the values and watch the effects

Answer 14

Okay Thanks love

Answer 15

you can see how each term affects the graph,

for yorus
f(x) = x3 − 18x2 + 107x − 210

a=1
b=-18
c=107
d=-210

probably have to zoom way out and set the scale on the axis to see it good

Answer 16

just describe what it looks like and why

Answer 17

For huge x values, the function f(x) goes off to +infinity
because
the coefficient on the x^3 term 'A' is positive...

Answer 18

to get the x intercepts, (must be at least one real value), solve for f(x) =0

if it is a book problem, that probably factors nicely so you can get nice values for x

Answer 19

f(x) = x3 − 18x2 + 107x − 210 = ( )*( )* ( ) = 0

( )*( )* ( ) = 0

you can tell from the graph with those values for B and C and D, it will have 3 x-intercepts, so it may factor into that form

Answer 20

for those x - intercept wouldnt it be (5,0) (6,0) (7,0)

Answer 21

@DanJS

Answer 22

yes, that factors nice into those 3 quantities

Answer 23

for f(x) =0, x can be 5, or 6 or 7

Answer 24

So for y it would be -210

Answer 25

yes, (0,y) , when x is zero

Answer 26

Maybe explain the end behavior for the graph when you let x be very large possitive and negative...

the larger x becomes, the more the x^3 term will completely dominate the value of f(x)

Answer 27

I just dont know how to put all that in an explanation does that make sense

Answer 28

for this one, as x becomes larger and larger, the values of f(x) also become larger and larger without bound, , same for -x, and f(x) going to huge - values

Answer 29

that explains the end behavior of the graph shooting upwards and downwards for ever to infinity

Answer 30

what class is this?

Answer 31

obviously its a math class lol

Answer 32

But for this last assignment I need to explain it but I swear I am horrible at explaining things

Answer 33

So this is so hard for me,

Answer 34

i mena, algebra, pre-calc, calculus
?

Answer 35

If you have to write it out, just go throgh all the posts from me above and should be enough

Answer 36

algebra 2