SOLUTION: I need a little help. Does this parabola open up/down or left/right? {{{Y^2}}} -{{{(x^2/4)}}} = 1

Algebra ->  Finance -> SOLUTION: I need a little help. Does this parabola open up/down or left/right? {{{Y^2}}} -{{{(x^2/4)}}} = 1      Log On


   

Question 1079778: I need a little help. Does this parabola open up/down or left/right?
Y%5E2 -%28x%5E2%2F4%29 = 1
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52898) About Me  (Show Source):
You can put this solution on YOUR website!
.
I need a little help. Does this parabola open up/down or left/right?
Y%5E2 -%28x%5E2%2F4%29 = 1
~~~~~~~~~~~~~~~~~~~~~~ 

Y%5E2 -%28x%5E2%2F4%29 = 1  --->

y%5E2 = 1+%2B+x%5E2%2F4  --->

y = +/- sqrt%281+%2B+x%5E2%2F4%29





Plots y = sqrt%281+%2B+x%5E2%2F4%29 (red) and y = -sqrt%281+%2B+x%5E2%2F4%29 (green)

It is not a parabola . . .


Actually, it is a hyperbola, instead.



Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!
I need a little help. Does this parabola open up/down or left/right?
Y%5E2 -%28x%5E2%2F4%29 = 1
y%5E2+-+x%5E2%2F4+=+1

4y%5E2+-+x%5E2+=+4 ------ Multiplying by LCD, 4

The COEFFICIENTS on the 2nd degree variables are DIFFERENT, and the signs on them (+ & -) are different also. Therefore, this is a HYPERBOLA.

Since the x term is NEGATIVE, this HYPERBOLA OPENS UP and DOWN (vertically).