Question 1658
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How do you graph the solution set for this quadratic inequality?:
`
y <u>></u> x<sup>2</sup> - 3x + 1
`<font color = "blue"><b>
You first graph the equation of the boundary equation, which is
found by replacing the inequality " <u>></u> " by an equal sign
" = ":  Since the inequality is " <u>></u> " rather than " > " we draw
the graph with a solid line. 
`
[When the inequality sign is " <u>></u> " or " <u><</u> ",
we draw the graph solid since it includes the boundary line, 
and when the inequality is " > " or " < " we draw it dashed or 
dotted].
`
So we wish to graph the boundary y = x<sup>2</sup> - 3x + 1
`
Make a table of points:
`
` x | y ` `|` `point` `|
` ----------------------
`-1 | 5 ` `|` (-1,5) ` |
` 0 | 1 ` `|` `(0,1) ` |
` 1 |-1 ` `|``(1,-1)` `| 
1.5 |-1.25 |(1.5,-1.25)|
` 2 |-1 ` `|` (2,-1)` `|
` 3 |`1 ` `|` `(3,1)` `|
` 4 |`5 ` `|` `(4,5)` `|
`
Plot these points and you get this graph
`
{{{graph(200,200,-2,5,-3,12,x^2-3x+1)}}} 
`
Now the rules for shading, which I can't do here, but which 
you can do on your paper are:
`
If the inequality is " > " or " <u>></u> ", then shade the area 
ABOVE the boundary graph.
`
If the inequality is " < " or " <u><</u> " then shade the area 
BELOW the boundary graph.
`
So since the inequality is " <u>></u> " you are to shade the area 
ABOVE (inside) the boundary graph drawn above. 
`
Edwin <font face = "wingdings" color = "red" size = 7>J</font></b>