calculusxy
  • calculusxy
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?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
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calculusxy
  • calculusxy
that seems like quadratic function, if i am not wrong. @Vocaloid
calculusxy
  • calculusxy
so it would be a parabola.
Vocaloid
  • Vocaloid
yes

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calculusxy
  • calculusxy
|dw:1443919129693:dw|
calculusxy
  • calculusxy
it's not the best graph, but would that be correct?
Vocaloid
  • Vocaloid
I think so, as long as the graph doesn't pass through the origin if c is positive, then the y-intercept should be something bigger than 0
calculusxy
  • calculusxy
but it does pass through the origin
Vocaloid
  • Vocaloid
hmmm then the answer is probably some other graph
Vocaloid
  • Vocaloid
is there list of choices?
calculusxy
  • calculusxy
yes
SolomonZelman
  • SolomonZelman
\(\large\color{black}{ \displaystyle f(x)=x^2+bx+c }\) \(\large\color{black}{ \displaystyle f(x)=\left(x^2+bx\right)+c }\) \(\large\color{black}{ \displaystyle f(x)=\left(x^2+bx+\frac{b^2}{4}\right)-\frac{b^2}{4}+c }\) \(\large\color{black}{ \displaystyle f(x)=\left(x+\frac{b}{2}\right)^2+\left(c-\frac{b^2}{4}\right) }\) 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)
calculusxy
  • calculusxy
SolomonZelman
  • SolomonZelman
If, c>b\(^2\)/4 then the shift is up. If, c
calculusxy
  • calculusxy
@SolomonZelman Sorry but i didn't quite understand what you were saying. i am in the beginning of 8th grade ...
SolomonZelman
  • SolomonZelman
I 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
  • SolomonZelman
Maybe a brief guide with rules of a shift of a function will help? \(\large\color{ teal }{\large {\bbox[5pt, lightcyan ,border:2px solid white ]{ \large\text{ }\\ \begin{array}{|c|c|c|c|} \hline \texttt{Shifts} ~~~\tt from~~~ {f(x)~~~\tt to~~~g(x)}&~\tt{c~~~units~~~~} \\ \hline \\f(x)= x^2 ~~~~~\rm{\Rightarrow}~~~~ g(x)= (x \normalsize\color{red}{ -~\rm{c} })^2 &~\rm{to~~the~~right~} \\ \text{ } \\ f(x)= x^2 ~~~~~\rm{\Rightarrow}~~~~ g(x)= (x \normalsize\color{red}{ +~\rm{c} })^2&~\rm{to~~the~~left ~} \\ \text{ } \\ f(x)= x^2 ~~~~~\rm{\Rightarrow}~~~~ g(x)= x^2 \normalsize\color{red}{ +~\rm{c} } &~\rm{up~} \\ \text{ } \\ f(x)= x^2 ~~~~~\rm{\Rightarrow}~~~~ g(x)= x^2 \normalsize\color{red}{ -~\rm{c} } &~\rm{down~} \\ \\ \hline \end{array} }}}\)
SolomonZelman
  • SolomonZelman
This is a rule where c denotes a positive number. (Any real number greater than 0)
calculusxy
  • calculusxy
i truly mean it. i don't understand anything that u just said
SolomonZelman
  • SolomonZelman
sorry
SolomonZelman
  • SolomonZelman
I 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
  • Vocaloid
well, let's review what we know so far
Vocaloid
  • Vocaloid
f(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?
calculusxy
  • calculusxy
yes
Vocaloid
  • Vocaloid
ok, now let's try plugging in x = 0 to find the y-intercept of the graph f(x) = x^2 + bx + c f(x) = 0^2 + b(0) + c = c so the y-intercept is (0,c), and since c is positive, the y-intercept should be positive
Vocaloid
  • Vocaloid
so, out of the 5 answer choices, only one is an upwards parabola with a positive y-intercept, which one is it?
calculusxy
  • calculusxy
would it be e?
Vocaloid
  • Vocaloid
yup! that's it
calculusxy
  • calculusxy
thanks!

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