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anonymous

  • 5 years ago

need to determine whether the graph of this equation opens upward or downward

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  1. anonymous
    • 5 years ago
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    \[y=(x-4)^{2}+5\]

  2. anonymous
    • 5 years ago
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    what equation?

  3. anonymous
    • 5 years ago
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    what class is this for?

  4. anonymous
    • 5 years ago
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    college algebra

  5. anonymous
    • 5 years ago
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    can you expand the right hand side?

  6. anonymous
    • 5 years ago
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    yes

  7. anonymous
    • 5 years ago
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    up

  8. anonymous
    • 5 years ago
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    For polynomials, the sign of the coefficient determines what way it opens.

  9. anonymous
    • 5 years ago
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    http://www.wolframalpha.com/input/?i=(x-4)^2%2B5

  10. anonymous
    • 5 years ago
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    you sure she knows which coefficient you are talking about? and is that an answer for college algbra? =/

  11. anonymous
    • 5 years ago
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    My bad, the leading coefficient.

  12. anonymous
    • 5 years ago
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    The graph is shifted units to the right, 5 units up and vertically stretched by a factor of 2

  13. anonymous
    • 5 years ago
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    I don't understand what astyria is asking? but thanks guys. I just wasn't sure if theres an easy way to tell from looking

  14. anonymous
    • 5 years ago
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    The graph is shifted 4 units to the right, 5 units up and vertically stretched by a factor of 2

  15. anonymous
    • 5 years ago
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    if i were you mary, I would plot some points (that's probably what you guys are learning)...i'm not sure if what cyter says makes sense to you...good luck

  16. anonymous
    • 5 years ago
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    Yeah, the graph someone attached helped. Thanks everyone

  17. anonymous
    • 5 years ago
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    take the second derivative of y or d²y/dx², if its positive, then the graph is concave up on an arbitrary interval (a,b)

  18. anonymous
    • 5 years ago
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    Cyter that is calculus. She is in college algebra.

  19. anonymous
    • 5 years ago
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    i now have to determine whither this point is wider or narrower. \[y=(x-4)^{2}+5\]

  20. anonymous
    • 5 years ago
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    The utmost easiest way to determine whether a graph of a polynomial opens up or down is to look at the leading coefficient, which is the coefficient in front of the x^2. If that coefficient is positive the graph opens up, if negative it opens down.

  21. anonymous
    • 5 years ago
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    oh ok. oops i typed the same problem. this is the equation I need to figure out if it is wider or narrower than the previous one..\[y=2(x-4)^{2}\]

  22. anonymous
    • 5 years ago
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    i think it's narrower

  23. anonymous
    • 5 years ago
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    The higher the magnitude of the coefficient, the narrower the graph is. You are correct.

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