Vertex of Parabola

[Guest]

I'm trying to do homework, but I can't figure this problem out. We didn't cover it in class and my book is so confusing that it's no help at all. I don't even know where to begin, so I'm hoping someone can explain this to me. Thank you in advance!

CONCEPT - Vertex of Parabola: Examine the quadratic equation y=ax^2+bx+1 where A is a positive real number and B is any real number. Use the vertex formula [-b/2a , 4ac-b^2/4a] to find the vertex (h, k) with the largest value of k for this family of parabolas. Find the value of k.

 

[topdawgizalaw]

u help me then i will help u, mine is the thread below yours

 

[stapel]

u help me then i will help u...

Please don't reply if you're not going to help. All this does is reduce the likelihood that the original poster will receive a reply.

Note to poster: Students are not required to answer other students' questions in order to receive replies to their own questions.

Examine the quadratic equation y=ax^2+bx+1 where A is a positive real number and B is any real number. Use the vertex formula [-b/2a , 4ac-b^2/4a] to find the vertex (h, k) with the largest value of k for this family of parabolas. Find the value of k.

I will assume, contrary to standard usage, that "A" is meant to be "a" and "B" is meant to be "b". You are given the formula "k = (4ac - b²)/4a", and are asked to find the largest value of k in the "family" of parabolas with c = 1. In other words, you have:

. . . . .k = (4a - b²)/4a = 1 - b²/4a

...and are asked to find the largest value of k possible. Clearly, the larger b²/4a is, the smaller k will be. So what is the smallest that b²/4a can be? (Hint: Think about the value of b.)

Eliz.

 

[Guest]

Thank you very much for your help.. I am trying very hard to understand this, but I really have no idea. I have given it quite a bit of thought, but b could be anything. :\

Examine the quadratic equation y=ax^2+bx+1 where A is a positive real number and B is any real number. Use the vertex formula [-b/2a , 4ac-b^2/4a] to find the vertex (h, k) with the largest value of k for this family of parabolas. Find the value of k.

I will assume, contrary to standard usage, that "A" is meant to be "a" and "B" is meant to be "b". You are given the formula "k = (4ac - b²)/4a", and are asked to find the largest value of k in the "family" of parabolas with c = 1. In other words, you have:

. . . . .k = (4a - b²)/4a = 1 - b²/4a

...and are asked to find the largest value of k possible. Clearly, the larger b²/4a is, the smaller k will be. So what is the smallest that b²/4a can be? (Hint: Think about the value of b.)

 

[stapel]

...b could be anything.

And the value of k would not change, regardless of the value of b? There is no value of b that would make b²/(4a) smaller than other values of b?

Eliz.

 

[Guest]

It's sad, but I honestly don't know.

 

[stapel]

What numbers have you tried?

Eliz.

 

[Guest]

What numbers have you tried?

None, because I still don't understand what I'm looking for. I'm sorry.. I'm honestly not being purposely obtuse, I just don't understand. :\

 

[stapel]

Well, try some numbers, and see what you get. Fix "a" at whatever value you feel like (since, in the end, this isn't the value that matters), and plug in various values for b. See what happens.

Eliz.

 

[Guest]

Well, try some numbers, and see what you get. Fix "a" at whatever value you feel like (since, in the end, this isn't the value that matters), and plug in various values for b. See what happens.

Eliz.

Thank you very much for your help, but I'm giving up on this one.. it makes no sense to me whatsoever.



-- Alena