Functions: Put y = x^2 - 4x - 5 into y = a(x - h)^2 + k form

S

stainedtears

New member
Joined
Sep 9, 2006
Messages
3
Hello.. I am taking an algebra class and I'm having problems with a certain question on some homework that is due in about 3 1/2 hours. I've been struggling with it for a while now and I've tried looking it up on several boards but havn't been successful.. I was hoping someone could help me please!

The question is:

For the function y = x^2 - 4x - 5, perform the following tasks:
a)Put the function in the form y = a(x - h)^2 + k
b)What is the equation for the line of symmetry for the graph of this function?

Ok, I've been stuck on part a so I haven't even gotten to part b yet. My book does not elaborate on the formula y = a(x - h)^2 + k so I have no idea where it came from or even what it is. I am familiar with solving quadratic equations using the 3 ways, and so far I have found that this problem has something to do with "completing the square" but I just can't figure it out..

Please help me, I would really appreciate it. I don't want just an answer, I want to know how to do it too. It doesn't help to have an answer and not be able to tell how you got it lol :shock:

Thank you so much in advance!! :)
 
That is the standard equation of a parabola.

You recognize the given quadratic as a parabola?. This is just completing the square.

\(\displaystyle x^{2}-4x-5=0\)

\(\displaystyle x^{2}-4x=5\)

Add the square of half the coefficient of x to both sides:

\(\displaystyle x^{2}-4x+4=9\)

Now, finish and recognize a, h, and k once you have the square completed.
 
Yes I have that answer as another part of the questoin.. so I have done the completing the square... I guess a better question would be, what is a, h, and k? I don't understand what the letters mean.

Are h and k the points of the vertex? and is a the orginal a from the ax^2 +bx+c?

If it is then I already have the answers I just didn't recognize them. If the above is right then a should be 1, h should be 2 and k is -9 right? I just have the place them in the formula?

Is this right? lol I'm sorry if I'm not being too clear right now. I'm very, very sleepy :(
 
You must log in or register to reply here.
Top