Parabola question

  • #1

Main Question or Discussion Point

mods please move this topic if this is not in the correct section. thanks. :)

the question is:
the vertices of the family of parabolas y = x^2 + bx, b is constant, lie on a single parabola. Find equation for that parabola.

my teacher require me to provide supporting details & background info that back up my answer and have to verify it using a different method. i'm really puzzled and i would greatly appreciate any help that comes my way. thanks in advance.
 

Answers and Replies

  • #2
Well why don't you start by showing what you've done on the problem, and we'll take it from there.
 
  • #3
HallsofIvy
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You might want to start by completing the square so it's easy to see where the vertices are.
 
  • #4
so this is what i've gotten so far, please correct me if i'm wrong.

for any generalized parabola, the equation is given in the standard form: y = ax^2 + bx + c

a = 1 (in the equation y = x^2 + bx)
b = constant
c = (b/2)^2

the equation for the parabola that the question asks for, if written as completing the square, should be: y - k = (x - h)^2.
we need to find the center (h, k) so that y = x^2 + bx.

y - k = (x - h)(x - h)
y - k = x^2 - 2xh + h^2

...?
 
  • #5
[tex]x^2+bx=(x+b/2)^2-b^2/4[/tex] check it and then see if that's helpful for you.
 
  • #6
HallsofIvy
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so this is what i've gotten so far, please correct me if i'm wrong.

for any generalized parabola, the equation is given in the standard form: y = ax^2 + bx + c

a = 1 (in the equation y = x^2 + bx)
Yes, but not in this equation! Would it be easier to write it as [itex]y= a(x^2+ (b/a)x)+ c[/itex]? How would you complete the square for [itex]a(x^2+ (b/a)x[/itex]?

b = constant
c = (b/2)^2

the equation for the parabola that the question asks for, if written as completing the square, should be: y - k = (x - h)^2.
we need to find the center (h, k) so that y = x^2 + bx.

y - k = (x - h)(x - h)
y - k = x^2 - 2xh + h^2

...?
Why, after completing the square, did you then ignore it?
 

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