What is the significance of the equation y=2(x-4)^2-3?

[DethRose]

Im In a 1st Year University math class and its been a while since i did this stuff and can't remember if I am doing this question right so any help would be much appreciated.

The question is to find all the info from the equation y=2(x-4)^2-3

I used the b+/- b^2 -4ac... equation and ended up getting 16+/- square root of 24/4.

This gives an odd number (5.22474, 2.77525) so i don't think it is right. When i apart the original equation to make into ax^2+bx+c=0 form i did 2(x^2-8x+16)-3=0 and i am not sure if that is correct either or if it should be multiplies without brackets.

Thanks for any help

 

[Gib Z]

I haven't checked your working out, but I don't see what's wrong with the numbers it gives? You were never given an indication the numbers would be pretty.

 

[Diffy]

The parabola you have is written in a very nice form...

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

"The question is to find all the info from the equation "... :-/

All the info? Be more specific. From this form it is easy to find the Vertex (h,k). You can also tell whether or not it will be opening up, or down. If a >0 then the parabola will open up. If a<0 then the parabola will be opening down.

Furthermore, a will tell you how thin or fat your parabola will be. If 0<|a|<1 your parabola will be fatter than the parabola y=x^2. If |a|>1 your parabola will be thinner than y = x^2.

As you can see one can tell a lot by the equation given without having to do much work. Is there further information that you need from the equation given? If so, what?