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Homework LogTues
12/8
Lesson Rev
Learning Objective: To remember everything in Chapter 4!
Hw: #411 P. 268 1 - 47 odd
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Homework LogThurs
12/10
Lesson Rev
Learning Objective: To remember everything in Chapter 4!
Hw: Quiz Correction
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Homework LogThurs
12/10
Lesson Rev
Learning Objective: To remember everything in Chapter 4!
Hw: Extra Credit WS
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12/8/15 Chapter 4 ReviewAdvanced Math/Trig
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Learning Objective
To remember everything in Chapter 4!
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Distance Formula1. Find the distance between (–7, –5) & (–8, 2)
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Distance Formula2. Find the shortest distance between (1, – 2) and the line x = –5. Find the distance
between (1, –2) and (–5, –2)
(1, –2)
x = –5
(–5, –2)
= = 6
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Graph3. a = –1 Opens leftVertex: (4, –1) AoS: y = – 1
x y
0 3
–3–2
3 0
01
V( 4 –1)
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Graph4. a = –1 Opens left = Vertex: (–1, 2) AoS: y = 2
x y
–5 –2
01
–2 –5
34
V(–1 2)
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Graph5. Get rad alone: Square both sides: Solve for x: a = 1, opens rightVertex (1, 2)
y – 2 0y 2
But original equation isn’t a parabola!
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Graph6. xSquare both sides: Solve for x: a = 1, opens up = Vertex (0, –2)
x 0But original equation isn’t a parabola!
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Graph7. Write an equation of the parabolaOpens up with V(–1, –3)Pick either of the other pts(1, 1) 1 = 4a – 3 a = 1
V(–1, –3)
(1, 1)(–3, 1)
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Graph8. Center (3, –1)Radius = = 4
(3, -1)
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Write an equation of a circle
9. Center (5, –2) radius 4
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Graph10. Square both sides: C(1, 0) r = 3
x – 1 0x 1
But original equation isn’t a circle!
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Test for Symmetry11. y–axis
x–axis
Origin
So it’s symmetric about the x–axis
NO!
Equivalent Eq’n! Yes!
NO!
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Transformation12. y = f (x) is shown.
Sketch y =
Sketch y = f (x) – 5
Sketch y = f (x + 7)
Sketch y = – f (x)
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Graph 13.
Major Axis: xMinor Axis: ya = b = c =
Center: (0, 0)Vertices: ()Co-Vertices: (Foci: (, 0)
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Graph14.
Major Axis: xMinor Axis: ya = b =
But original equation isn’t an ellipse4y 0y 0
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Write an Equation of the Ellipse Shown
15. Major Axis: yMinor Axis: xa = b =
(–3, 0) (3, 0)
(0, –5)
(0, 5)
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Graph 16. 288 288 288
Opens: ya = b = 3 c =5
C (0, 0) V () F ()
Asym: y =
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Graph 17. Opens xa = b = 3
But original eq’n isn’t a hyperbola x 0
V (–7.5, 0)
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Write an Equation of the Hyperbola Shown
18. Opens ya = b =
(–2, 0) (2, 0)
(0, –3)
(0, 3)
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Graph 19.
Major Axis: yMinor Axis: xa = 6 b = 4 c =
C (3, –1)V ()V (3, –7)CV (–1, –CV (7, –1)F (3, )
(3, –1)
(7, –1)
(–1, –1)
(3, 5)
(3, –7)
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Graph 20.
Opens: xa = 3 b = 2 c =
C (0, 1)V (–) V (3, 1)F (–)
(0, 1) (3, 1)(–3, 1)
(0 , 3)
(0, –1)
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Write a standard equation
21. Write a standard equation of an ellipse with C(–1, –3) and V(–1, 1) and
V(–1, –7) and endpoints of minor axis at (–4, –3)
& (2, –3)Major: y Minor: xa = 4 b = 3
3
4
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Find Inverse22. 4x – 3y = 12
4x – 12 = 3y
It’s a straight line, (not horizontal), so it’s 1–1
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Verify Inverses22.
Show
=() – 4
= x + 4 – 3
= x
Show
=() + 3
= x – 3 + 3
= x
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Ratios23. Express 45 km per hour in terms of cm per minute.
1 km = 1000 m
1 m = 100 cm
1 hour = 60 min
= 75,000 cm/min
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Ratios24. If a mixture contains 40% water, how many ounces of water are in 15 ounces of the mixture?
Word ratio
100x = 40(15)
100x = 600 6 oz of water
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Variations25. Suppose z varies jointly as x and and inversely as 2w – 1. If z = 4 when x = –2, t = 1, and w = 5, find z when x = –3, t = 4, and w = –1.
k = –18
z = –448
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Rewrite in Standard Form.
Identify the conic
26. __+ _ _
1 44 –36
HyperbolaOpens: xa = 3 b = 2Center (–1, –2)
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Rewrite in Standard Form.
Identify the conic
27. ____
16 16
ParabolaOpens DownVertex (4, –3)AoS: x = 4
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Rewrite in Standard Form.
Identify the conic
28. __+ __ _
4 3616 256
EllipseMajor: xa = 4 b = 3Center (2, –4)
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Rewrite in Standard Form.
Identify the conic
29. __+ __ 9CircleCenter (–2, 3)Radius =
4 49 9