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Analytical Geometry

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If the line y=ax+b and the parabola y=a(x-h) ... Analytical Geometry Author: Jeffrey Harvey Last modified by: Jeff Harvey Created Date: 3/8/2014 7:22:45 PM – PowerPoint PPT presentation

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Title: Analytical Geometry


1
World 3-4 Graphing Inequalities
2
Recall that an inequality contains the symbols
_________
lt,gt,, and
If the line yaxb and the parabola ya(x-h)2k
can be graphed,
so too can y lt ax b and y
a(x-h)2 k!
The solution set is a region of space where the
inequality relation holds true.
Eg. 1
Sketch y gt 2x 1
Solution Set Set of all possible solutions
Dashed line states that y cannot equal 2x1, only
values greater (gt) than that.
3
Sketch
Eg. 2
Recall that (5,0) and (0,2) are the x and y
intercepts.
CHECK shading
sub in (0,0)
Solution Set
Since 0 IS less than 1. (0,0) is in the solution
set and the shading is below the line.
4
Eg. 3
Sketch 3x 6y 12 0, Rearrange first
3x - 6y 12 0
- 12
- 12
-3x
-3x
-6y -3x - 12
-6
-6
Solution Set
y 1x 2 2
Check with (0,0)
Math Gods
3x - 6y 12 0
When you divide by a negative switch the
direction of the inequality symbol.
3(0) 6(0) 12 0
12 0
True! so we shaded properly
5
Eg. 4
Sketch the parabola y 0.5(x-2)(x4)
Find the vertex
Xsymmetry
-1
2(-4) 2
y 0.5(x-2)(x4)
y 0.5((-1)-2)((-1)4)
y 0.5(-3)(3)
y -4.5
Check shading with (0,0)
y 0.5(x-2)(x4)
y 0.5(0-2)(04)
False! 0 is not -4 so (0,0) is not in the set
and we shaded properly.
0 0.5(-2)(4)
0 -4
6
Homework
World 3-4 Graphing handouts Finish last page on
World 3-3
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