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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?

Mathematics
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complete the square for x^2 + dx +3d to get its vertex
mukushla is right :) try doing ...
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?

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Other answers:

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
Thanks! I'll try it again.
in 1st case the value of d=0 and 3 in 2nd case d=1/3 and -1/3
@jenejij take a look http://www.mathsisfun.com/algebra/completing-square.html
Oh okay. I know how to "complete the square" haha. Got it. =)
Thanks everyone =)
Actually - still having problems.. =/ I don't think x=3. x= 0, and x= 12.
x=12 is not right answer
thats what the answer in the back of my text book is... but I don't know how to get there.
what is the final answer of first part?
d = 0 and d= 12. According the the textbook...
and for second part ??
\[d = + or - 2 / \sqrt{13}\]
wait
I got the answer: plz check it
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
to find y ordinate substitute this value in the given eq. we have |dw:1341572810912:dw|
|dw:1341572956794:dw|
I circled that thing.. is it d?
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
yes it is d
have u understood ??
yes Thank you!!!
similarly u can do second part .. plz do it and tell me have u got the answer or not
okay I will work on it
give me a medal .........lol
\[x^2 + 3dx - d^2 +1 then 0 = (-d/2)^2 +3d(-d/2) - d^2 + 1 \]
\[(d/4)^2 + -3d^2/2 -d^2 +1 = 0 \]
no; for second part u again need to find the x coordinate and follow the same steps
since it was a different equation
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
no problem: from which country u r from ??
US.
okay so then is 3d = -b/2a?
no. wait.
I can't think. I have to do this in the morning. Thanks so far.
give me 1 min, let me tell you
in second part : a=1 b=3d c=1 now subs. in -b/2a u have -3d/2
okay. I was on the right track. but not quite there.
hmm
then put this value of x in original equation x^2+3dx+1=0|dw:1341574077931:dw|
Okay. I see the answer. And I understand, but without sleep I won't reeeally get it. Again thank you for your help.
bye i had sent u mail plz check it

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