Jeff Bivin -- LZHS Last Updated: March 11, 2008 Section 10.2.
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Jeff Bivin -- LZHS Last Updated: March 11, 2008 Section 10.2
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Transcript of Jeff Bivin -- LZHS Last Updated: March 11, 2008 Section 10.2.
Jeff Bivin -- LZHSLast Updated: March 11, 2008
Section 10.2
Jeff Bivin -- LZHS
Parabola
The set of all points that are equidistant from a given point (focus) and a given line (directrix).
Jeff Bivin -- LZHS
Parabola
Distance between focus and vertex = p
Distance between vertex and directrix = p
apnote4
1: cbxaxy 2
Jeff Bivin -- LZHS
ParabolaThe line segment through the focus
perpendicular to the axis of symmetry with endpoints on the parabola is called the
Latus Rectum (LR)
Length of the LR = 4p
Jeff Bivin -- LZHS
Graph the following parabola
y = 3x2 + 24x + 53
y = 3(x2 + 8x ) + 53
y + 48 = 3(x2 + 8x + (4)2) + 53
y = 3(x + 4)2 + 5
Axis of symmetry: x = -4
Vertex: (-4, 5)
y = 3(x2 + 8x + (4)2) + 53 - 48
3●(4)2 = 48
x + 4 = 0
Jeff Bivin -- LZHS
Graph the following parabola
y = 3(x + 4)2 + 5
Axis of symmetry: x = -4
Vertex: (-4, 5)
Jeff Bivin -- LZHS
Graph the following parabolay = 3(x + 4)2 + 5
Axis of symmetry: x = -4
Vertex: (-4, 5)
Focus:
1215,4
Directrix: 12114y
Length of LR:
121
)3(41
41 ap
121
121 5,45,4
1215 y
31
12144 p
Jeff Bivin -- LZHS
Graph the following parabola
y = -2x2 + 12x + 11
y = -2(x2 - 6x ) + 11
y - 18 = -2(x2 - 6x + (-3)2) + 11
y = -2(x - 3)2 + 29
Axis of symmetry: x = 3
Vertex: (3, 29)
y = -2(x2 - 6x + (-3)2) + 11 + 18
-2●(-3)2 = -18
x - 3 = 0
Jeff Bivin -- LZHS
Graph the following parabolay = -2(x - 3)2 + 29
Axis of symmetry: x = 3
Vertex: (3, 29)
Focus:
8728,3
Directrix:
8129y
Length of LR:
81
)2(41
41
ap
8129,3
8129y
21
8144 p
Jeff Bivin -- LZHS
Graph the following parabola
x = y2 + 10y + 8
x = (y2 + 10y ) + 8
x + 25 = (y2 + 10y + (5)2) + 8
x = (y + 5)2 - 17
Axis of symmetry: y = -5
Vertex: (-17, -5)
x = (y2 + 10y + (5)2) + 8 - 25
(5)2 = 25
y + 5 = 0
Jeff Bivin -- LZHS
Graph the following parabolax = (y + 5)2 - 17
Axis of symmetry: y = -5
Vertex: (-17, -5)
Focus:
5,16 43
Directrix:
4117x
Length of LR:
41
)1(41
41 ap
5,17 41
4117 x 144 41 p
Jeff Bivin -- LZHS
Graph the following parabola
x = -2y2 - 8y - 1
x = -2(y2 + 4y ) - 1
x - 8 = -2(y2 + 4y + (2)2) - 1
x = -2(y + 2)2 + 7
Axis of symmetry: y = -2
Vertex: (7, -2)
x = -2(y2 + 4y + (2)2) - 1 + 8
-2(2)2 = -8
y + 2 = 0
Jeff Bivin -- LZHS
81
)2(41
41
ap
Graph the following parabolax = -2(y + 2)2 + 7
Axis of symmetry: y = -2
Vertex: (7, -2)
Focus:
2,6 87
Directrix:
8
17x
Length of LR:
2,7 81
817x
21
8144 p
Jeff Bivin -- LZHS
Graph the following parabola
y = 5x2 - 30x + 46
y = 5(x2 - 6x ) + 46
y + 45 = 5(x2 - 6x + (-3)2) + 46
y = 5(x - 3)2 + 1
Axis of symmetry: x = 3
Vertex: (3, 1)
y = 5(x2 - 6x + (-3)2) + 46 - 45
5●(-3)2 = 45
x - 3 = 0
Jeff Bivin -- LZHS
Graph the following parabolay = 5(x - 3)2 + 1
Axis of symmetry: x = 3
Vertex: (3, 1)
Focus:
2011,3
Directrix: 2019y
Length of LR:
201
)5(41
41 ap
2011,3
2011y
51
20144 p
Jeff Bivin -- LZHS
Graph the following parabola
x = y2 - 4y + 11
x = (y2 - 8y ) + 11
x + 8 = (y2 - 8y + (-4)2) + 11
x = (y - 4)2 + 3
Axis of symmetry: y = 4
Vertex: (3, 4)
x = (y2 - 8y + (-4)2) + 11 - 82
12
12
1
2
1
2
1
8)16(2
1
y - 4 = 0
Jeff Bivin -- LZHS
Graph the following parabolax = (y - 4)2 + 3
Axis of symmetry: y = 4
Vertex: (3, 4)
Focus:
Directrix:
Length of LR:
2
1
4,3 21
212x
21
)(41
41
21 ap
4,3 21
213 x
244 21 p
Jeff Bivin -- LZHS
A Web Site & Sketchpad demo• http://www.xahlee.org/SpecialPlaneCurves_dir/Parabola_dir/parabolaReflect.mov
• A sketchpad demo:
Jeff Bivin -- LZHS
