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

How do geometric relationships and measurements help us to solve problems and make sense of our world?
How do we use math models to describe physical relationships?

Essential Questions for the course

How is this similar or different from what I have done before?
What can I do to retain what I have learned?
Does my answer make sense? If not, what do I do?
Do I need help, and where do I go to find it?
How would a calculator make this problem easier to do?
How do I explain or justify my work to myself and others?
What is the given information and how do I use it?

LEARNING TARGET QUIZ SCORING RUBRIC

4MASTERY

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.

3DEVELOPING MASTERY

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

2BASIC 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.

1MINIMAL 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.

0NO 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:

What can I do to retain what I have learned?

Learning Targets:

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) B)

C) D)

E) F)

9-1-1 Homework Worksheet Complete the Square

1. 2.

3. 4.

5. 6.

7. 8.

9. 10.

9.1 Warm Up(s)

Complete the square.

Date ______

Notes: 9-1

Essential Questions:

How do geometric relationships and measurements help us to solve problems and make sense of our world?
How do we use math models to describe physical relationships?

Learning Targets:

From an equation, I can identify the vertex, directrix, and focus of a parabola and sketch the graph.
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 symmetricwith 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 theaxis, 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 Homeworkpg 637 1-17 odd

9.1 Warm Up(s)

Given find the vertex, focus, directrix, and graph the parabola.

Given , find the vertex, focus, directrix, and graph the parabola.

Date ______

Notes: 9-1

Essential Questions:

How do geometric relationships and measurements help us to solve problems and make sense of our world?
How do we use math models to describe physical relationships?

Learning Targets:

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

Worksheet9-1 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

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

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

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:

How do geometric relationships and measurements help us to solve problems and make sense of our world?
How do we use math models to describe physical relationships?

Learning Targets:

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

Given , find the center and radius of the circle. Sketch the graph

9-2 Warm Up(s)

Date ______

Notes: 9-2

Essential Questions:

How do geometric relationships and measurements help us to solve problems and make sense of our world?
How do we use math models to describe physical relationships?

Learning Targets:

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:______

Major Axis: Horizontal or Vertical

Vertices:______

Co-vertices: ______

Foci: ______

Center:______

Major Axis: Horizontal or Vertical

Vertices:______

Co-vertices: ______

Foci: ______

You Try: c)

Center:______

Major Axis: Horizontal or Vertical

Vertices:______

Co-vertices: ______

Foci: ______

Day 2

Center:______

Major Axis: Horizontal or Vertical

Vertices:______

Co-vertices: ______

Foci: ______

Center:______

Major Axis: Horizontal or Vertical

Vertices:______

Co-vertices: ______

Foci: ______

Center:______

Major Axis: Horizontal or Vertical

Vertices:______

Co-vertices: ______

Foci: ______

You try: g)

Center:______

Major Axis: Horizontal or Vertical

Vertices:______

Co-vertices: ______

Foci: ______

Example 2: Write the equation of an ellipse from a graph.

Homework 9-2 Day 1 Pg 446 1-7, 9 skip the eccentricity

Homework 9-2 Day 2 Pg 646 13, 14, 17

Worksheet Mixed Practice Circles and Ellipses(9-2)

Continue Worksheet Mixed Practice Circles and Ellipses(9-2)

9-3 Warm Ups

Date ______

Notes: 9-3

Essential Questions:

How do geometric relationships and measurements help us to solve problems and make sense of our world?
How do we use math models to describe physical relationships?

Learning Targets:

I can write equations of hyperbolas in standard form.

A hyperbola is the set of all points (x, y) the difference of whose distances from two distinct fixed points (foci) is constant.

Standard Form Equations:

Horizontal transverse axis

Vertical transverse axis

Center
Transverse axis
Vertices
Foci
Asymptotes

Example 1: Find center, vertices, foci, and asymptotes. Sketch graph.

Center
Transverse axis
Vertices
Foci
Asymptotes

Example 2: Write the equation of a hyperbola from the graph.

Classifying Conics

What do you look for in an equation to classify it as a circle, ellipse, parabola, or hyperbola?

Parabola:______

Circle:______

Ellipse:______

Hyperbola:______

Example 3: Classify as a parabola, circle, ellipse, or hyperbola.

1) ______

2) ______

3) ______

4) ______

5) ______

6) ______

7) ______

8) ______

9) ______

10) ______

9-3 Worksheet

Sketch the graph of the hyperbola in exercises 11 – 15.

Continue 9-3 Worksheet

Find an equation in standard from for the hyperbola that satisfies the given conditions.

Find the center, vertices, and the foci of the given hyperbola.

Graph the hyperbola. Identify its vertices and foci.

49.

Worksheet Mixed Review for all Conic Sections (9-1 to 9-3 and Circles)

Continue Worksheet Mixed Review for all Conic Sections (9-1 to 9-3 and Circles)

Domino Effect Review 9.1-9.3

Use the k value to fill in #2.

Use the h value to fill in #3.

Use the x value of the center to fill in #4.

Use the “p” value to fill in #5.

Chapter 9 Test Review Sheet

Put the equations in standard form.

1) 2)

3) 4)

Chapter 9 Test Review Sheet Continued

5) Find an equation of the parabola with vertex at (2, 1) and directrix at x = -1

6) Find the standard form of the ellipse satisfying the given condition:

Foci: (0, 3), (4, 3)

Major Axis of Length 6

7) Find the standard form of the equation of the hyperbola satisfying the following conditions:

Vertices: ( 3 , -2), (3 , 10)

Foci: (3, -6), (3, 14)

8) The jet of a water fountain forms a parabola. Write an equation for the path of the parabola the water follows.

Chapter 9 Test Review Sheet Continued

9) Circle the equation that represents the given conic section.

10) Write the equation of the given conic section.

Chapter 9 Test Review Sheet Continued

Sketch each graph. List all important information.

11)

Vertex:______

Focus:______

Directrix:______

Axis of Symmetry: Vertical or Horizontal

Opens: Up Down Left Right

12)

Center:______

Radius:______

Chapter 9 Test Review Sheet Continued

13)

Center:______

Major Axis: Horizontal or Vertical

Vertices:______

Co-vertices: ______

Foci: ______

14)

Center:______

Transverse Axis: horizontal or vertical

Vertices: ______

Foci: ______

Asymptotes:______

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