Learning Targets and Homework Assignments

Chapter 9

Conic Sections

Johnson and Prange

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Learning Targets and Homework Assignments

Learning Target / Practice for the Learning Target / Score on Learning Target Quiz / Help needed? yes/no
9.1.1 / I can write the equation of a parabola in standard form by completing the square. / worksheet
9.1.2 / From an equation, I can identify the vertex, directrix, and focus of a parabola and sketch the graph. / pg 637 1-17 odd
9.1.3 / I can write the equation of the parabola in standard form given various pieces of information about the parabola. / pg 637 25 - 45 odd
none / I can write the equation of a circle in standard form. / worksheet
9.2.1 / I can write equations of ellipses in standard form. / Day 1 pg 646 1-7, 9 skip the eccentricity
Day 2 Pg 646 13, 14, 17
9.3.1 / I can write equations of hyperbolas in standard form. / worksheet
9.3.2 / I can classify conics from an equation written in standard form. / worksheet

Essential Questions for the chapter

1. How do geometric relationships and measurements help us to solve problems and make sense of our world?

2. How do we use math models to describe physical relationships?

Essential Questions for the course

1. How is this similar or different from what I have done before?

2. What can I do to retain what I have learned?

3. Does my answer make sense? If not, what do I do?

4. Do I need help, and where do I go to find it?

5. How would a calculator make this problem easier to do?

6. How do I explain or justify my work to myself and others?

7. What is the given information and how do I use it?

LEARNING TARGET QUIZ SCORING RUBRIC

4 MASTERY

I completely understand the strategy and mathematical operations to be used, and I used them correctly.

· My work shows what I did and what I was thinking while I worked the problem.

· The way I worked the problem makes sense and is easy for someone else to follow.

· I followed through with my strategy from beginning to end.

· My explanation and work was clear and organized.

· I did all of my calculations correctly.

3 DEVELOPING MASTERY

I completely understand the strategy and mathematical operations to be used, but a minor error kept me from completing the problem correctly.

2 BASIC UNDERSTANDING

I used mathematical operations and a strategy that I think works for most of the problem.

· Someone might have to add information for my explanation to be easy to follow.

· I know which operations I should have used, but couldn’t complete the problem.

· I think I know what the problem is about, but I might have a hard time explaining it.

· I’m not sure how much detail I need in order to help someone understand what I did.

· I made several calculation errors.

1 MINIMAL UNDERSTANDING

I wasn’t sure which mathematical operations to use, and my plan didn’t work.

· I tried several things, but didn’t get anywhere.

0 NO EVIDENCE
I left the problem blank.

· I didn’t know how to begin.

· I don’t know what to write.

· I provided no evidence of understanding.

Conic Section Formula Sheet

Parabola: Ellipse:

vertical

horizontal

Circle:

Hyperbola:

horizontal

vertical

9.1 Warm Up(s)

Date ______

Notes: 9-1

Essential Questions:

1. What can I do to retain what I have learned?

Learning Targets:

1. I can write the equation of a parabola in standard form by completing the square.

Example 1 In each of the following problems, complete the square. This is a skill that will be needed in order to graph parabolas from an equation written in standard form.

A) x2+8x-y+11=0 B) y2+10y-x+18=0

C) x2-16x-5y-26=0 D) x2-4x-7y-17=0

E) y2-2y+3x+10=0 F) y2-3y+4x-13.75=0

9-1-1 Homework Worksheet Complete the Square

1. x2-2x-y-24=0 2. x2-4x-y-32=0

3. x2+4x-y-2=0 4. y2+2y-x-1=0

5. x2-4x-6y-20=0 6. y2+2y-x+1=0

7. y2-10y-x+2=0 8. x2-2x-13y-38=0

9. x2+5x-2y+0.25=0 10. y2+7y-x-1=0

9.1 Warm Up(s)

Complete the square.

1. x2+2x-y+3=0 2. y2-4y-8x+20=0

3. x2+6x-2y+1=0

Date ______

Notes: 9-1

Essential Questions:

1. How do geometric relationships and measurements help us to solve problems and make sense of our world?

2. How do we use math models to describe physical relationships?

Learning Targets:

1. From an equation, I can identify the vertex, directrix, and focus of a parabola and sketch the graph.

2. I can write the equation of the parabola in standard form given various pieces of information about the parabola.

Conics: ______

Conic Sections: ______

A parabola is the set of all points (x, y) equidistant from a fixed line (directrix) and a fixed point (focus) not on the line.

Important Ideas to Remember

1. A parabola is symmetric with respect to its axis.

2. The directrix is parallel to the x or y axis.

3. The vertex is the midpoint between the focus and the directrix.

4. The focus and the directrix lie on the axis, p units from vertex.

5. Standard Forms of the Equations

What is the purpose of the focus and directrix? (patty paper demonstration)

Example 1: Find the vertex, focus, directrix of the parabola and sketch its graph.

Vertex:______

Focus:______

Directrix:______

Axis of Symmetry: Vertical or Horizontal

Opens: Up Down Left Right

Vertex:______

Focus:______

Directrix:______

Axis of Symmetry: Vertical or Horizontal

Opens: Up Down Left Right

Vertex:______

Focus:______

Directrix:______

Axis of Symmetry: Vertical or Horizontal

Opens: Up Down Left Right

Vertex:______

Focus:______

Directrix:______

Axis of Symmetry: Vertical or Horizontal

Opens: Up Down Left Right

Vertex:______

Focus:______

Directrix:______

Axis of Symmetry: Vertical or Horizontal

Opens: Up Down Left Right

9-1-2 Homework pg 637 1-17 odd

9.1 Warm Up(s)

1. Given y+22=-16x+3 find the vertex, focus, directrix, and graph the parabola.

2. Given x+42=-6y+1, find the vertex, focus, directrix, and graph the parabola.

Date ______

Notes: 9-1

Essential Questions:

1. How do geometric relationships and measurements help us to solve problems and make sense of our world?

2. How do we use math models to describe physical relationships?

Learning Targets:

1. I can write the equation of the parabola in standard form given various pieces of information about the parabola.

Example 1: Find the standard form of the equation of the parabola with vertex at the origin.

A) Focus: (0, 1) B) Focus:

C) D) Vertical axis and passes

through the point (-3,-3)

Example 2: Find the standard form of the equation of the parabola.

E) Vertex: ( -2, 1) & Directrix: x = 1

F) Vertex: (3, -3) & Focus

9-1-3 Homework pg 637 25 - 45 odd

Worksheet 9-1 mixed practice

Continue Worksheet 9-1 mixed practice

“Gateway to the West”

The St. Louis “Gateway Arch” is one of the most famous and recognizable landmarks in the United States. Known as the “Gateway to the West” due to its proximity in the Midwest, this Arch has many interesting facts.

Directions: Using research materials (including the internet), answer the following questions below. Even though the Arch is very close but not actually a parabola, for our mathematical purposes we will assume that it is.

1) What is the maximum height of the Arch (in feet)? ______

2) What is the outer width (“base”) of the Arch? ______

3) What type of “shape” is the Arch? ______

4) Calculate the mathematical equation of the Arch assuming that is

parabolic (which it is not) in shape. Show all work below and draw a diagram of the Arch with dimensions below. Equation must be given in exact form. No decimals.

Sketch the graph and use the y-axis as the axis of symmetry and the x-axis as the ground. Use the parabola equation in vertex form:

______

Based on your answer in #4, what is the height of the Arch when standing……… (Show all work below!!) Round each answer to the nearest hundredth.

5) 50 feet from under the center of the Arch? 5) ______

6) 100 feet from under the center of the Arch? 6) ______

7) 250 feet from under the center of the Arch? 7) ______

8) You are standing on the ground looking at a point

on the arch that is 50 high. How far from

under the center of the arch are you standing? 8)______

9) What type of material was used in Arch exterior? ______

10) There are trams that transport people to the top of the Arch. ______

What is the capacity of people per tram or “capsule?”

11) How far does each capsule travel from the start to the top of the arch? ______

12) Who was the architect of the Arch? ______

13) Where and when was he born? ______

14) When was the Arch’s dedication for its completion? ______

15) What resources did you use to find this information? If the internet was used, write the actual website(s) below.

9-1 Warm Ups

1. Write the equation of the parabola in standard form given a focus at (-2, 4) and directrix at y = 6.

2. Given a focus at (-5, 0) and a directrix at x = 1, write the equation of the parabola.

3. Write the equation of the parabola in standard form given a focus at (3, 5) and directrix at y = 1.

Date ______

Notes: not in the book

Essential Questions:

1. How do geometric relationships and measurements help us to solve problems and make sense of our world?

2. How do we use math models to describe physical relationships?

Learning Targets:

1. I can write equations of circles in standard form.

Definition of a Circle:

Standard form:

Example: Put the equation in standard form. Find the center & radius. Sketch graph too.

A) B)

Example 2: The point (0,6) is on the circle centered at (-3,2).

A) Write the standard form equation.

B) Sketch the graph.

C) Find the area.

D) Find the circumference.

Example 3:

A) Write the equation of the circle from a graph.

B) Write the equation of the circle from a graph.

Circle Worksheet

In problems 1-6, write each equation in standard form. Identify the center, radius, and sketch graph.

1) 2)

3) 4)

Continue Circle Worksheet

5) 6)

7) Write an equation of the circle that has center (-4, 5) and radius of

8) Write an equation of a circle centered at the origin and passing through (6, 8).

9) Write an equation of the circle with endpoints of its diameter at (0,0) and (10,0).

Continue Circle Worksheet

10) The point (13, 9) is on a circle centered at (7, 1).

A) Write an equation for the circle. B) Sketch the graph.

C) Find the area. D) Find the circumference.

11) Write the standard equation of a circle whose center is (-3,7) and whose diameter is 12.

A. (x -3) + (y+7) = 12

B. (x +3) + (y – 7) = 144

C. (x+3) + (y – 7) = 6

D. (x+3) + (y – 7) = 36

12) Which is the equation for the graph shown below?

Circle Warm Ups

1. Given x2-8x+y2-12y-12=0, find the center and radius of the circle. Sketch the graph

9-2 Warm Up(s)

Date ______

Notes: 9-2

Essential Questions:

1. How do geometric relationships and measurements help us to solve problems and make sense of our world?

2. How do we use math models to describe physical relationships?

Learning Targets:

1. I can write equations of ellipses in standard form.

Definition of an Ellipse:

General Sketch of Ellipse:

Standard Form Equations of an Ellipse:

Other Important Information for Ellipses:

Example 1: Sketch the graph of each ellipse.

Center:______