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?

Question

anonymous · Answer

complete the square for x^2 + dx +3d to get its vertex

anonymous · Answer

mukushla is right :)
try doing ...

anonymous · Answer

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?

anonymous · Answer

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

anonymous · Answer

Thanks! I'll try it again.

anonymous · Answer

in 1st case the value of d=0 and 3
in 2nd case d=1/3 and -1/3

anonymous · Answer

@jenejij take a look http://www.mathsisfun.com/algebra/completing-square.html

anonymous · Answer

Oh okay. I know how to "complete the square" haha. Got it.  =)

anonymous · Answer

Thanks everyone =)

anonymous · Answer

Actually - still having problems.. =/ I don't think x=3. x= 0, and x= 12.

anonymous · Answer

x=12 is not right answer

anonymous · Answer

thats what the answer in the back of my text book is... but I don't know how to get there.

anonymous · Answer

what is the final answer of first part?

anonymous · Answer

d = 0 and d= 12. According the the textbook...

anonymous · Answer

and for second part ??

anonymous · Answer

$$d = + or - 2 / \sqrt{13}$$

anonymous · Answer

wait

anonymous · Answer

I got the answer: plz check it

anonymous · Answer

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

anonymous · Answer

to find  y ordinate substitute this value in the given eq. we have |dw:1341572810912:dw|