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neverforgetvivistee

  • 3 years ago

can someone please help me in understanding graphing quadratic inequalities? look at this (answers are below) http://www.kutasoftware.com/FreeWorksheets/Alg1Worksheets/Graphing%20Quadratic%20Inequalities.pdf what does the solid/shaded line mean? Why is it shaded in and some are shaded out? I know how to get the coordinates by plugging in random x values, but I don't know about anything else.

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  1. asnaseer
    • 3 years ago
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    ok, in general, lets say you have some function in the form:\[y=f(x)\]and you have some inequality like:\[y>=4\]

  2. asnaseer
    • 3 years ago
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    now, on the line \(y=f(x)\) you know the value of 'y' will EQUAL the value of 'f(x)', so we draw the curve for y=f(x) as a solid line to indicate that we need to include this region.

  3. asnaseer
    • 3 years ago
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    so now we need to consider the line y=4. this will be a horizontal line which passes through y=4.

  4. asnaseer
    • 3 years ago
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    the horizontal line could intersect the curve at some points. e.g.: |dw:1322436287068:dw|

  5. asnaseer
    • 3 years ago
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    now since our inequality is y>=4, we need to draw a solid line at the places where y=4.

  6. asnaseer
    • 3 years ago
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    |dw:1322436426127:dw|

  7. neverforgetvivistee
    • 3 years ago
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    but what about the shaded region?

  8. asnaseer
    • 3 years ago
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    sorry - my explanation went a bit hay wire above!

  9. asnaseer
    • 3 years ago
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    what I should have said is lets say we have an inequality of the form y>=f(x)

  10. neverforgetvivistee
    • 3 years ago
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    lol it's okay take your time :)

  11. asnaseer
    • 3 years ago
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    now, on the curve y=f(x), we know it satisfies the inequality - so we make the line solid

  12. asnaseer
    • 3 years ago
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    below the curve y=f(x) does NOT satisfy the inequality as there we have y<f(x)

  13. asnaseer
    • 3 years ago
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    above the curve y=f(x) DOES satisfy the inequality, so we include that region by shading it in

  14. neverforgetvivistee
    • 3 years ago
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    for shading it in, how do you know it satisfies the inequality?

  15. asnaseer
    • 3 years ago
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    |dw:1322436711384:dw|

  16. asnaseer
    • 3 years ago
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    does the diagram make sense?

  17. neverforgetvivistee
    • 3 years ago
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    not really :(

  18. asnaseer
    • 3 years ago
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    I have taken some point x=x1 (which is represented by the vertical line) where this vertical line crosses the curve y=f(x), we know y=f(x1) above that point of intersection, we know y>f(x1) below that point of intersection, we know y<f(x1)

  19. neverforgetvivistee
    • 3 years ago
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    thanks :)

  20. asnaseer
    • 3 years ago
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    np - sorry for the confusion at the beginning :-)

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