jenejij
If the graph of the quadratic function f(x) = x^2 + dx +3d has its vertex on the x axis what are the possible values of d? What if f(x) = x^2 + 3dx +1?
Delete
Share
This Question is Closed
mukushla
Best Response
You've already chosen the best response.
1
complete the square for x^2 + dx +3d to get its vertex
meera_yadav
Best Response
You've already chosen the best response.
1
mukushla is right :)
try doing ...
jenejij
Best Response
You've already chosen the best response.
1
I have the answers. Easily accessible in the back of the book. How to solve it is the problem. When you say complete the square what do you mean? I've been trying x^2 + dx +3d = ax^2 + (-2ah)x+ (ah^2+k) And trying to identify the vertex.. that waayy... But what do you mean by complete the square?
k.rajabhishek
Best Response
You've already chosen the best response.
1
the vertex of quadratic equation is given by (-b/2a, c-b^2/4a)
since it has vertex on X axis therefore y ordinate =0 .
hence c-b^2=0
jenejij
Best Response
You've already chosen the best response.
1
Thanks! I'll try it again.
k.rajabhishek
Best Response
You've already chosen the best response.
1
in 1st case the value of d=0 and 3
in 2nd case d=1/3 and -1/3
jenejij
Best Response
You've already chosen the best response.
1
Oh okay. I know how to "complete the square" haha. Got it. =)
jenejij
Best Response
You've already chosen the best response.
1
Thanks everyone =)
jenejij
Best Response
You've already chosen the best response.
1
Actually - still having problems.. =/ I don't think x=3. x= 0, and x= 12.
k.rajabhishek
Best Response
You've already chosen the best response.
1
x=12 is not right answer
jenejij
Best Response
You've already chosen the best response.
1
thats what the answer in the back of my text book is... but I don't know how to get there.
k.rajabhishek
Best Response
You've already chosen the best response.
1
what is the final answer of first part?
jenejij
Best Response
You've already chosen the best response.
1
d = 0 and d= 12. According the the textbook...
k.rajabhishek
Best Response
You've already chosen the best response.
1
and for second part ??
jenejij
Best Response
You've already chosen the best response.
1
\[d = + or - 2 / \sqrt{13}\]
k.rajabhishek
Best Response
You've already chosen the best response.
1
wait
k.rajabhishek
Best Response
You've already chosen the best response.
1
I got the answer: plz check it
k.rajabhishek
Best Response
You've already chosen the best response.
1
the value of x coordinate of vertex is given by -b/2a;
from the given question we have a=1
b=d
c=3d
substituting the values in -b/2a we have -d/2
k.rajabhishek
Best Response
You've already chosen the best response.
1
to find y ordinate substitute this value in the given eq. we have |dw:1341572810912:dw|
jenejij
Best Response
You've already chosen the best response.
1
|dw:1341572956794:dw|
jenejij
Best Response
You've already chosen the best response.
1
I circled that thing.. is it d?
k.rajabhishek
Best Response
You've already chosen the best response.
1
since it has vertex on x axis thus y=0
hence we have
d^2/4 - d^2/2 +3d = 0
on solving we have d=0 and 12
k.rajabhishek
Best Response
You've already chosen the best response.
1
yes it is d
k.rajabhishek
Best Response
You've already chosen the best response.
1
have u understood ??
jenejij
Best Response
You've already chosen the best response.
1
yes
Thank you!!!
k.rajabhishek
Best Response
You've already chosen the best response.
1
similarly u can do second part ..
plz do it and tell me have u got the answer or not
jenejij
Best Response
You've already chosen the best response.
1
okay I will work on it
k.rajabhishek
Best Response
You've already chosen the best response.
1
give me a medal .........lol
jenejij
Best Response
You've already chosen the best response.
1
\[x^2 + 3dx - d^2 +1 then 0 = (-d/2)^2 +3d(-d/2) - d^2 + 1 \]
jenejij
Best Response
You've already chosen the best response.
1
\[(d/4)^2 + -3d^2/2 -d^2 +1 = 0 \]
k.rajabhishek
Best Response
You've already chosen the best response.
1
no;
for second part u again need to find the x coordinate and follow the same steps
k.rajabhishek
Best Response
You've already chosen the best response.
1
since it was a different equation
jenejij
Best Response
You've already chosen the best response.
1
okay let me try again. toss that grain of salt my way (I've been working all night.. it's 4:21 am) I'm not usually this bad haha
k.rajabhishek
Best Response
You've already chosen the best response.
1
no problem:
from which country u r from ??
jenejij
Best Response
You've already chosen the best response.
1
US.
jenejij
Best Response
You've already chosen the best response.
1
okay so then is 3d = -b/2a?
jenejij
Best Response
You've already chosen the best response.
1
no. wait.
jenejij
Best Response
You've already chosen the best response.
1
I can't think. I have to do this in the morning. Thanks so far.
k.rajabhishek
Best Response
You've already chosen the best response.
1
give me 1 min, let me tell you
k.rajabhishek
Best Response
You've already chosen the best response.
1
in second part :
a=1
b=3d
c=1
now subs. in -b/2a u have -3d/2
jenejij
Best Response
You've already chosen the best response.
1
okay. I was on the right track. but not quite there.
jenejij
Best Response
You've already chosen the best response.
1
hmm
k.rajabhishek
Best Response
You've already chosen the best response.
1
then put this value of x in original equation x^2+3dx+1=0|dw:1341574077931:dw|
jenejij
Best Response
You've already chosen the best response.
1
Okay. I see the answer. And I understand, but without sleep I won't reeeally get it. Again thank you for your help.
k.rajabhishek
Best Response
You've already chosen the best response.
1
bye
i had sent u mail
plz check it