Homework LogTues

12/8

Lesson Rev

Learning Objective: To remember everything in Chapter 4!

Hw: #411  P. 268 1 - 47 odd

Homework LogThurs

12/10

Lesson Rev

Learning Objective: To remember everything in Chapter 4!

Hw: Quiz Correction

Homework LogThurs

12/10

Lesson Rev

Learning Objective: To remember everything in Chapter 4!

Hw: Extra Credit WS

12/8/15 Chapter 4 ReviewAdvanced Math/Trig

Learning Objective

To remember everything in Chapter 4!

Distance Formula1. Find the distance between (–7, –5) & (–8, 2)

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

Graph3. a = –1 Opens leftVertex: (4, –1) AoS: y = – 1

x y

0 3

–3–2

3 0

01

V( 4 –1)

Graph4. a = –1 Opens left = Vertex: (–1, 2) AoS: y = 2

x y

–5 –2

01

–2 –5

34

V(–1 2)

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!

Graph6. xSquare both sides: Solve for x: a = 1, opens up = Vertex (0, –2)

x 0But original equation isn’t a parabola!

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)

Graph8. Center (3, –1)Radius = = 4

(3, -1)

Write an equation of a circle

9. Center (5, –2) radius 4

Graph10. Square both sides: C(1, 0) r = 3

x – 1 0x 1

But original equation isn’t a circle!

Test for Symmetry11. y–axis

x–axis

Origin

So it’s symmetric about the x–axis

NO!

Equivalent Eq’n! Yes!

NO!

Transformation12. y = f (x) is shown.

Sketch y =

Sketch y = f (x) – 5

Sketch y = f (x + 7)

Sketch y = – f (x)

Graph 13.

Major Axis: xMinor Axis: ya = b = c =

Center: (0, 0)Vertices: ()Co-Vertices: (Foci: (, 0)

Graph14.

Major Axis: xMinor Axis: ya = b =

But original equation isn’t an ellipse4y 0y 0

Write an Equation of the Ellipse Shown

15. Major Axis: yMinor Axis: xa = b =

(–3, 0) (3, 0)

(0, –5)

(0, 5)

Graph 16. 288 288 288

Opens: ya = b = 3 c =5

C (0, 0) V () F ()

Asym: y =

Graph 17. Opens xa = b = 3

But original eq’n isn’t a hyperbola x 0

V (–7.5, 0)

Write an Equation of the Hyperbola Shown

18. Opens ya = b =

(–2, 0) (2, 0)

(0, –3)

(0, 3)

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)

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)

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

Find Inverse22. 4x – 3y = 12

4x – 12 = 3y

It’s a straight line, (not horizontal), so it’s 1–1

Verify Inverses22.

Show

=() – 4

= x + 4 – 3

= x

Show

=() + 3

= x – 3 + 3

= x

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

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

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

Rewrite in Standard Form.

Identify the conic

26. __+ _ _

1 44 –36

HyperbolaOpens: xa = 3 b = 2Center (–1, –2)

Rewrite in Standard Form.

Identify the conic

27. ____

16 16

ParabolaOpens DownVertex (4, –3)AoS: x = 4

Rewrite in Standard Form.

Identify the conic

28. __+ __ _

4 3616 256

EllipseMajor: xa = 4 b = 3Center (2, –4)

Rewrite in Standard Form.

Identify the conic

29. __+ __ 9CircleCenter (–2, 3)Radius =

4 49 9