sleepyjess
  • sleepyjess
More College Algebra! yay... I'm still having trouble with finding the equation of a parabola when the vertex is not at the origin. Example problem below
Algebra
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
amistre64
  • amistre64
consider = a ^2
amistre64
  • amistre64
, represent the 'modified origin'
amistre64
  • amistre64
but hurry up with the example :)

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

sleepyjess
  • sleepyjess
Question: Find an equation of the parabola with vertex at (-2, 3) and focus at (0, 3). Solution Given: The vertex (-2, 3) and focus (0, 3) both lie on the horizontal like y = 3 (the axis of symmetry). The distance \(\it a\) from the vertex to the focus is a = 2. Also, because the focus lies to the right of the vertex, the parabola opens to the right. Consequently, the form of the equation is \((y-k)^2 = 4a(x-h)\)
sleepyjess
  • sleepyjess
Sorry, was having some internet issues :)
sleepyjess
  • sleepyjess
How did they get that a = 2?
amistre64
  • amistre64
do you know how to move a point?
sleepyjess
  • sleepyjess
I don't think so
amistre64
  • amistre64
add something to it ...
sleepyjess
  • sleepyjess
Do I just need to make the -2 in the vertex 0 to find \(\it a\)?
amistre64
  • amistre64
we are given 2 points vertex at (-2, 3) and focus at (0, 3) spose we move them so the focus is at the origin (0,0) ... we would translate all points as (x+0,y-3) vertex at (-2+0, 3-3) and focus at (0+0, 3-3) vertex at (-2,0) and focus at (0,0) how far is the vertex -2 from the focus 0?
amistre64
  • amistre64
or zeroing out the vertex is fine too ... the distance would remain the same
sleepyjess
  • sleepyjess
2, so however far away the x-coordinate of the vertex is from the x-coordinate of the focus would be a?
amistre64
  • amistre64
depends on direction, but yes
sleepyjess
  • sleepyjess
Okay, I think I can do this now :)
amistre64
  • amistre64
if we zero out one point, the other will tell us how far they are from one another
amistre64
  • amistre64
v=(2,5) f=(2,-2) whats the distance and direction between them?
amistre64
  • amistre64
zero one of them out (move it to the origin) v=(2, 5) f=(2,-2) -2-5 -2 -5 ----------------- v=(0,0) f=(0,-7) -7 tells us the focus is under the vertex, and is 7 units away
sleepyjess
  • sleepyjess
ooohhh, that seems really simple, I was looking at the formulas for the equations and going "what am I supposed to use???"
sleepyjess
  • sleepyjess
Random problem from the book: v (4, -2) f (6, -2) v = (4, -2) f = (6, -2) -4, +2 -4, +2 --------------------------- v = (0, 0) f = (2, 0) So the focus is 2 units from the vertex? And 2 would be a?
amistre64
  • amistre64
very good, and the parabola opens up ... the focus is 2 above the vertex
sleepyjess
  • sleepyjess
Yay! :)
amistre64
  • amistre64
err, 2 to the right ... opens to the right
sleepyjess
  • sleepyjess
haha that's what I was about to say :P
sleepyjess
  • sleepyjess
Thank you :3
amistre64
  • amistre64
:) the voices in my head like to tell me when im wrong
amistre64
  • amistre64
goodluck
sleepyjess
  • sleepyjess
Well they must not speak very often since you're so smart :)

Looking for something else?

Not the answer you are looking for? Search for more explanations.