A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 4 years ago

At what point does the normal line to the curve y = x^2-3 at (1, -2) intersect the curve a second time? The derivative is 2x so the slope at (1, -2) is 2 thus the equation of the tangent line is y+2 = 2 ( x-1) which I can graph both of, and am still not seeing where it crosses twice: http://www.wolframalpha.com/input/?i=y%2B2+%3D+2+%28+x-1%29+and+y+%3D+x%5E2-3

  • This Question is Closed
  1. Rogue
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[y = x^2 - 3\]\[\frac {dy}{dx} = 2x\]\[y' (1) = 2\]\[Y _{tangent}^{} = 2(x-1)-2\] The normal line to the curve is perpendicular to the curve, so it has the negative reciprocal slope of the tangent.\[Y _{normal}^{} = \frac {-1}{2}(x-1)-2\]So now just set Ynorm equal to y = x^2 - 3 to find the other coordinate. My tangent and normal line equations are in the linearization form by the way, you can simplify them down if you want.

  2. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Negative reciprocal! Geesh. That helps! Thanks!

  3. Rogue
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Hehe, well, now you know :)

  4. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    err ok so I set -1/2(x-1)-2 = x^2-3 and eventually got x^2+1/2x - 3/2 which, when I put in 1 for x, I get 0 out which is evidently not correct. I guess I am still confused after all :/

  5. Rogue
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[Y _{norm}^{} = -0.5x -1.5\]\[Y = x^2 - 3\]\[0 = x^2 - 3 + 0.5x + 1.5 = x^2 + 0.5x - 1.5\] Solving for that should give you the other solution, which is -1.5. I think you just made a computation error somewhere, no biggie.

  6. Rogue
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Oh, you put 1 into that... No...

  7. Rogue
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    When you set Ynorm = Y, you are finding when the 2 graphs intersect. Its not the derivative or anything, so you don't plug in 1. You already know that they intersect at the point given to you, (1,-2). You just have to find the other point. Solving for that equation will give you x = 1, x = -1.5. So the other coordinate where the normal & the parabola intersects has a x-coordinate of -1.5 Plugging in -1.5 into either equations will give us the y coordinate, which is -0.75. So the other point where the normal intersects the curve is (-1.5, -0.75).

  8. Rogue
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Do you get it, or need a bit more explanation?

  9. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I'm sorry, reviewing now, had a kid wake up with a bad dream -_-

  10. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Thank you!!! I /do/ understand!! I have no idea how I would've gotten that without your help.

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

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.