anonymous
  • anonymous
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.
Mathematics
chestercat
  • chestercat
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asnaseer
  • asnaseer
ok, in general, lets say you have some function in the form:\[y=f(x)\]and you have some inequality like:\[y>=4\]
asnaseer
  • asnaseer
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.
asnaseer
  • asnaseer
so now we need to consider the line y=4. this will be a horizontal line which passes through y=4.

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asnaseer
  • asnaseer
the horizontal line could intersect the curve at some points. e.g.: |dw:1322436287068:dw|
asnaseer
  • asnaseer
now since our inequality is y>=4, we need to draw a solid line at the places where y=4.
asnaseer
  • asnaseer
|dw:1322436426127:dw|
anonymous
  • anonymous
but what about the shaded region?
asnaseer
  • asnaseer
sorry - my explanation went a bit hay wire above!
asnaseer
  • asnaseer
what I should have said is lets say we have an inequality of the form y>=f(x)
anonymous
  • anonymous
lol it's okay take your time :)
asnaseer
  • asnaseer
now, on the curve y=f(x), we know it satisfies the inequality - so we make the line solid
asnaseer
  • asnaseer
below the curve y=f(x) does NOT satisfy the inequality as there we have y
asnaseer
  • asnaseer
above the curve y=f(x) DOES satisfy the inequality, so we include that region by shading it in
anonymous
  • anonymous
for shading it in, how do you know it satisfies the inequality?
asnaseer
  • asnaseer
|dw:1322436711384:dw|
asnaseer
  • asnaseer
does the diagram make sense?
anonymous
  • anonymous
not really :(
asnaseer
  • asnaseer
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
anonymous
  • anonymous
thanks :)
asnaseer
  • asnaseer
np - sorry for the confusion at the beginning :-)

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