A community for students.
Here's the question you clicked on:
 0 viewing
calculusxy
 one year ago
If the function f is defined by f(x) = x^2 + bx + c, where b and c are positive constants, which could be the graph of f?
calculusxy
 one year ago
If the function f is defined by f(x) = x^2 + bx + c, where b and c are positive constants, which could be the graph of f?

This Question is Closed

calculusxy
 one year ago
Best ResponseYou've already chosen the best response.0that seems like quadratic function, if i am not wrong. @Vocaloid

calculusxy
 one year ago
Best ResponseYou've already chosen the best response.0so it would be a parabola.

calculusxy
 one year ago
Best ResponseYou've already chosen the best response.0dw:1443919129693:dw

calculusxy
 one year ago
Best ResponseYou've already chosen the best response.0it's not the best graph, but would that be correct?

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.2I think so, as long as the graph doesn't pass through the origin if c is positive, then the yintercept should be something bigger than 0

calculusxy
 one year ago
Best ResponseYou've already chosen the best response.0but it does pass through the origin

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.2hmmm then the answer is probably some other graph

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.2is there list of choices?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1\(\large\color{black}{ \displaystyle f(x)=x^2+bx+c }\) \(\large\color{black}{ \displaystyle f(x)=\left(x^2+bx\right)+c }\) \(\large\color{black}{ \displaystyle f(x)=\left(x^2+bx+\frac{b^2}{4}\right)\frac{b^2}{4}+c }\) \(\large\color{black}{ \displaystyle f(x)=\left(x+\frac{b}{2}\right)^2+\left(c\frac{b^2}{4}\right) }\) So, we see a shift to the left by b/2 units, and a shift vertically (whether up or down depends on whether b²/4 is greater smaller or equal to c)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1If, c>b\(^2\)/4 then the shift is up. If, c<b\(^2\)/4 then the shift is down. If, c=b\(^2\)/4 then no vertical shift.

calculusxy
 one year ago
Best ResponseYou've already chosen the best response.0@SolomonZelman Sorry but i didn't quite understand what you were saying. i am in the beginning of 8th grade ...

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1I just completed the square, that is all. And now you have two possible answers for your problems (again depending on which is greater c or b\(^2\)/4).

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1Maybe a brief guide with rules of a shift of a function will help? \(\large\color{ teal }{\large {\bbox[5pt, lightcyan ,border:2px solid white ]{ \large\text{ }\\ \begin{array}{cccc} \hline \texttt{Shifts} ~~~\tt from~~~ {f(x)~~~\tt to~~~g(x)}&~\tt{c~~~units~~~~} \\ \hline \\f(x)= x^2 ~~~~~\rm{\Rightarrow}~~~~ g(x)= (x \normalsize\color{red}{ ~\rm{c} })^2 &~\rm{to~~the~~right~} \\ \text{ } \\ f(x)= x^2 ~~~~~\rm{\Rightarrow}~~~~ g(x)= (x \normalsize\color{red}{ +~\rm{c} })^2&~\rm{to~~the~~left ~} \\ \text{ } \\ f(x)= x^2 ~~~~~\rm{\Rightarrow}~~~~ g(x)= x^2 \normalsize\color{red}{ +~\rm{c} } &~\rm{up~} \\ \text{ } \\ f(x)= x^2 ~~~~~\rm{\Rightarrow}~~~~ g(x)= x^2 \normalsize\color{red}{ ~\rm{c} } &~\rm{down~} \\ \\ \hline \end{array} }}}\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1This is a rule where c denotes a positive number. (Any real number greater than 0)

calculusxy
 one year ago
Best ResponseYou've already chosen the best response.0i truly mean it. i don't understand anything that u just said

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1I didn't know you are unfamiliar with completing the square, or perhaps my presenation of it was poor. I apologize again:( Good luck tho (but, a side note there are 2 possible answers to your problem)

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.2well, let's review what we know so far

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.2f(x) = x^2 + bx + c, b and c are positive constants, correct? since the coefficient on x^2 is positive (1), we know that the parabola must face upwards, with me so far?

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.2ok, now let's try plugging in x = 0 to find the yintercept of the graph f(x) = x^2 + bx + c f(x) = 0^2 + b(0) + c = c so the yintercept is (0,c), and since c is positive, the yintercept should be positive

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.2so, out of the 5 answer choices, only one is an upwards parabola with a positive yintercept, which one is it?
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.