× Didn't find what you were looking for? Ask a question
Top Posters
Since Sunday
5
o
5
4
m
4
b
4
x
4
a
4
l
4
t
4
S
4
m
3
s
3
New Topic  
patrick19 patrick19
wrote...
Posts: 86
Rep: 1 0
3 years ago
a) y = x(x-4)(x-1)
-> 3
-> positive
-> x = 4, 1 (zero's)
-> y = 0(0-4)(0-1) (y-intercept)
  = 0
-> 4 + 1/2 = 2.5 -> -5.63 (min)
This is what I did, in order to sketch the graph and I just wanted to know if I did my calculations right before I graph the whole thing, because my textbook doesn't show the full answer to this.
Read 238 times
19 Replies

Related Topics

Replies
wrote...
Valued Member
Educator
3 years ago
Start by solving all zeros... Notice that the function is completely factored, which makes it easy, especially for a cubic. You solve by setting y = 0

0 = x(x-4)(x-1)

0 = x

0 = x - 4
x = +4

0 = x - 1
x = +1

Therefore, the function crosses:

(0, 0), (4, 0), and (1, 0)

Next, find the y-intercept, by setting x = 0. You should get a y-intercept at (0, 0)

Now determine the end behavior of the function (video link below). You need to write it in standard form, so multiply all factors out:

y = x(x-4)(x-1)
y = (x^2 - 4x)(x - 1)
y = x^3 - x^2 -4x^2 + 4x
y = x^3 - 3x^2 + 4x

The highest degree given that it is a cubic - if you multiply it all out - is 3. 3 is odd. The leading coefficient is also positive, therefore the end behavior will move up on the right side. Since the highest power is odd, it'll go down to left.

My sketch is shown below:



Video on end behavior:



Video on solving cubics:

patrick19 Author
wrote...
3 years ago
how about finding the estimated max and min values?
wrote...
Valued Member
Educator
3 years ago
For that, take the average between each zero.

For example, the average between 0 and 1 is 0.5. The average between 1 and 4 is 2.5. Substitute those values into the function, and you'll get your estimated max and min values
patrick19 Author
wrote...
3 years ago
for both max and min? because that's usually for finding only min and that's what I did above, not sure if it is right though.
wrote...
Valued Member
Educator
3 years ago
Yes, it should help you find both. Sub those values in, get an output. You should get an estimate of what the local max or min is
patrick19 Author
wrote...
3 years ago
Okay so by doing that I got a result of -5.63 for both the max and min, would you agree?
wrote...
Valued Member
Educator
3 years ago
This is more in line of what I was thinking


patrick19 Author
wrote...
3 years ago
Sorry for the late reply, I believe I got it now, I did all of c) and just wanted to know if I did it correctly, since my textbook answers are confusing/inaccurate. 
 Attached file 
Thumbnail(s):
You must login or register to gain access to this attachment.
wrote...
Valued Member
Educator
3 years ago
Looking good, but did you see that the multiplicity the zero (3, 0) is 2? In case you're curious:

 Attached file 
Thumbnail(s):
You must login or register to gain access to this attachment.
patrick19 Author
wrote...
3 years ago
Yes I did notice that, thanks Slight Smile
wrote...
Valued Member
Educator
3 years ago
Mark as solved?
patrick19 Author
wrote...
3 years ago Edited: 3 years ago, patrick19
One more thing, how about if it was a quartic function and there is a variety of zero's, how would you find the max and min once again? Like for example for c) I ended up getting 0,0, -1/2, 3, 5.
Post Merge: 3 years ago

and also when finding the max and min with the zero's does it matter what zero you're using to find it, I think that's where I'm getting confused.
wrote...
Valued Member
Educator
3 years ago
Hi patrick19

You'd do something like this:





  New Topic      
Explore
Post your homework questions and get free online help from our incredible volunteers
  1094 People Browsing
Related Images
  
 827
  
 5
  
 250
Your Opinion
What's your favorite funny biology word?
Votes: 156