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candyfloss94

  • 3 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.

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  1. anonymous
    • 3 years ago
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    you are being told in a round about way that the vertex is \((-2,4)\)

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

  3. anonymous
    • 3 years ago
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    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
    • 3 years ago
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    how come the vertex is (-2,4)? what does the vertical axis of symmetry x= -2 mean?

  5. anonymous
    • 3 years ago
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    |dw:1353124009816:dw|

  6. anonymous
    • 3 years ago
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    means a) the parabola is symmetric about the line \(x=-2\) and b) the first coordinate of the vertex is \(-2\)

  7. anonymous
    • 3 years ago
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    the fact that the range is \([4\infty)\) tells you the second coordinate of the vertex is \(4\)

  8. candyfloss94
    • 3 years ago
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    I see...that's what I don't know before. I just know that there is a line x=-2

  9. candyfloss94
    • 3 years ago
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    |dw:1353124262023:dw| if I may ask more, if the graph's like this, how would you say it in words?

  10. anonymous
    • 3 years ago
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    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. anonymous
    • 3 years ago
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    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. anonymous
    • 3 years ago
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    sorry i meant "the axis of symmetry would be a horizontal line" not the "vertex" that makes no sense

  13. candyfloss94
    • 3 years ago
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    how about the vertex for my second example? is it something like..(-2,0)?

  14. candyfloss94
    • 3 years ago
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    anyway, big thanks for ur help @satellite73

  15. candyfloss94
    • 3 years ago
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    I mean, if the axis of symmetry is y=2, then the vertex would be (-2,2), is this right?

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