A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
Esmeralda and Heinz are working to graph a polynomial function, f(x). Esmeralda says that the thirddegree polynomial has four intercepts. Heinz argues that the function only crosses the xaxis three times. Is there a way for them both to be correct? Explain your answer.
I really need help! Please :) I am desperate :(
anonymous
 one year ago
Esmeralda and Heinz are working to graph a polynomial function, f(x). Esmeralda says that the thirddegree polynomial has four intercepts. Heinz argues that the function only crosses the xaxis three times. Is there a way for them both to be correct? Explain your answer. I really need help! Please :) I am desperate :(

This Question is Closed

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0To answer this question, think about how and when a polynomial function crosses the xaxis.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I don't know anything about polynomial functions and have to complete this course this week!

cwrw238
 one year ago
Best ResponseYou've already chosen the best response.0well one of the intercepts could be through the yaxis

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0A polynomial function crosses the xaxis at its roots.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0That is, for example, \[f(x) = ax^3+bx^2+cx+d = 0\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@math1234 so Heinz is correct?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The roots of a polynomial function are the values of x such that \[f(x) = 0\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Now, notice that a norder polynomial can have at most n roots at any time.

cwrw238
 one year ago
Best ResponseYou've already chosen the best response.0Esmerelda didn't say the intercepts were on the x axis only . The 3 roots will be at xintercepts but its possible that the graph cuts theyaxis as well

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes, exactly. I wanted to paint that point in the end.

cwrw238
 one year ago
Best ResponseYou've already chosen the best response.0 that way they can both be right

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So there is a way for them both to be correct because Esmeralda says they can cross four times and heinz just says it crosses the x 3 times

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0First, do you understand that a nordered polynomial can have at most n roots, meaning at most n xaxis intercepts?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Good, then consider the yintercept. Polynomials must cross the y axis at some point as they are infinitely continuous.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Furthermore, they can only cross the yaxis exactly once.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Otherwise, it will violate the straight line test.

cwrw238
 one year ago
Best ResponseYou've already chosen the best response.0 because a 3rd degree polynomial might only cross the x  axis once  it might only have 1 real root The other 2 will be complex .

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0therefore only Esmeralda is right because heinz says it only crosses the x three times. not the y at all right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Not just in the complex case. A 3rd order polynomial can have less xaxis intercepts due to repeated roots.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay, so then what is the next step?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0To conclude, the answer to your question is that both propositions are correct.

cwrw238
 one year ago
Best ResponseYou've already chosen the best response.0No  they are both right because Heinz only refers to the xaxis.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay ? could y'all help with questions related to this?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thank you !! @cwrw238 could you help more?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@math1234 could you help more with related question?

cwrw238
 one year ago
Best ResponseYou've already chosen the best response.0I would but gotta go right now sorry
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.