Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

candyfloss94

  • 2 years ago

Find the equation of a quadratic function f whose graph has a vertical axis of symmetry x = -2, the range of f is given by the interval [4 , +infinity) and f(2) = 8.

  • This Question is Open
  1. satellite73
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    you are being told in a round about way that the vertex is \((-2,4)\)

  2. satellite73
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    this means it looks like \(y=a(x+2)^2+4\) the only number you do not know is \(a\)

  3. satellite73
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    but you can solve for it, since \[f(2)=8\]you know \(8=a(2+2)^2+4\) and so \[16a+4=8\] \[16a=4\] \[a=\frac{1}{2}\]

  4. candyfloss94
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    how come the vertex is (-2,4)? what does the vertical axis of symmetry x= -2 mean?

  5. satellite73
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1353124009816:dw|

  6. satellite73
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    means a) the parabola is symmetric about the line \(x=-2\) and b) the first coordinate of the vertex is \(-2\)

  7. satellite73
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    the fact that the range is \([4\infty)\) tells you the second coordinate of the vertex is \(4\)

  8. candyfloss94
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I see...that's what I don't know before. I just know that there is a line x=-2

  9. candyfloss94
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1353124262023:dw| if I may ask more, if the graph's like this, how would you say it in words?

  10. satellite73
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes but you can see it from the picture right? vertex is right on the axis of symmetry, so if it is \(x=-2\) then so is the first coordinate of the vertex

  11. satellite73
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    in your second example the parabola opens to the right, so the vertex would be a horizontal line, not a vertical one it would be something like \(y=2\)

  12. satellite73
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    sorry i meant "the axis of symmetry would be a horizontal line" not the "vertex" that makes no sense

  13. candyfloss94
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    how about the vertex for my second example? is it something like..(-2,0)?

  14. candyfloss94
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    anyway, big thanks for ur help @satellite73

  15. candyfloss94
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I mean, if the axis of symmetry is y=2, then the vertex would be (-2,2), is this right?

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

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

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.