Learning Goal:

Students will understand the meaning of a parabola and demonstrate this knowledge by being able to graph the parabola and write the equation of the parabola graphed.

Agenda:

1. Prior knowledge check and introduction

2. Large group activity modeling problems on the activity

3. Activity on Vocabulary.

4. Worksheet activity in partners.

5. Homework

6. Quiz tomorrow to confirm understanding.

Learning Goal:

Students will understand the meaning of a parabola and demonstrate this knowledge by being able to graph the parabola and write the equation of the parabola graphed.

Sketch the graph to the right with a focus and directrix are graphed. Use your graph to answer the following.

(Remember, this is a check of prior knowledge, if you have no

idea of the answer, put “no idea”.)

1. Graph the parabola on the graph. Label the vertex, focus, directrix, and latus rectum.

2. Write the equation of the parabola in standard form.

3. Write the equation of the red line:

We will begin with “parabolas”!

Precalculus by Carter, Cuevas, Day, Malloy, Bryan, Holliday, and Hovsepian; Glencoe McGraw Hill

This is one of many uses of parabolas.

Can you see the parabolas?

Solar Collectors

Precalculus by Carter, Cuevas, Day, Malloy, Bryan, Holliday, and Hovsepian; Glencoe McGraw Hill

Learning Goal:

Students will understand the meaning of a parabola and demonstrate this knowledge by being able to graph the parabola and write the equation of the parabola graphed.

A parabola is a locus of points in a plane that are equidistant from a fixed point, called the focus, and a specific line called the directrix.

A parabola is symmetric about the line perpendicular to the directrix through the focus called the axis of symmetry. The vertex is the intersection of the parabola and the axis of symmetry.

On the next slide, students will identify points on the parabola by individuals coming to the screen and selecting a point equidistant from the directrix and focus.

Use the circles to determine the distance from the focus. Use the rectangular grid to determine the distance from the directrix. Remember, they should be the same!

Learning Goal:

Students will understand the meaning of a parabola and demonstrate this knowledge by being able to graph the parabola and write the equation of the parabola graphed.

A parabola is a locus of points in a plane that are equidistant from a fixed point, called the focus, and a specific line called the directrix.

A parabola is symmetric about the line perpendicular to the directrix through the focus called the axis of symmetry. The vertex is the intersection of the parabola and the axis of symmetry.

The latus rectum is a segment through the focus that has a length four times the distance from the vertex to the focus.

p is the directed distance from the vertex to the focus.

Precalculus by Carter, Cuevas, Day, Malloy, Bryan, Holliday, and Hovsepian; Glencoe McGraw Hill

Learning Goal:

Students will understand the meaning of a parabola and demonstrate this knowledge by being able to graph the parabola and write the equation of the parabola graphed.

For the graph to the right, label and identify:

focus:

directrix:

vertex:

axis of symmetry:

p =

latus rectum length

As a class:

Learning Goal:

Students will understand the meaning of a parabola and demonstrate this knowledge by being able to graph the parabola and write the equation of the parabola graphed.

For the parabola

Point: (x, y) is any point on the parabola

vertex: (h, k)

p =

focus:

directrix:

axis of symmetry:

latus rectum length

Information needed to determine the orientation

(which way it opens) of the parabola.

Learning Goal:

Students will understand the meaning of a parabola and demonstrate this knowledge by being able to graph the parabola and write the equation of the parabola graphed.

The equation of the parabola: 2

4x h p y k 24y k p x h

p > 0 parabola opens up

p < 0 parabola opens down

p > 0 parabola opens right

p < 0 parabola opens left

What do we need to know to determine the

equation of the parabola?

Opens:

Vertex:

p =

Equation:_________________________________

Learning Goal:

Students will understand the meaning of a parabola and demonstrate this knowledge by being able to graph the parabola and write the equation of the parabola graphed.

On the next slide, students will identify points on the parabola by individuals coming to the screen and selecting a point equidistant from the directrix and focus.

Use the circles to determine the distance from the focus. Use the rectangular grid to determine the distance from the directrix. Remember, they should be the same!

Precalculus by Carter, Cuevas, Day, Malloy, Bryan, Holliday, and Hovsepian; Glencoe McGraw Hill

Graph the parabola given the focus and directrix:

Write the equation of this parabola:

Complete:Opens:__________p = ______Vertex:______Focus:_______Directrix:________Length of latus rectum: _______(Axis of Symmetry:__________)

Learning Goal:

Students will understand the meaning of a parabola and demonstrate this knowledge by being able to graph the parabola and write the equation of the parabola graphed.

Given Focus and Directrix, determine the equation of the parabola:

Focus: (2, 3) Directrix: y = − 1

-10 -8 -6 -4 -2 2 4 6 8 10

-10

-8

-6

-4

-2

2

4

6

8

10

Opens:Vertex:p =

Learning Goal:

Students will understand the meaning of a parabola and demonstrate this knowledge by being able to graph the parabola and write the equation of the parabola graphed.

Mat Activity:

Students receive their mat and solution squares to fill in the missing squares. Students should randomly place their answer squares around the mat before moving the answer square to the appropriate place.

Notice, each vocabulary word to the left has a definition and picture.

The third column should have the appropriate answers placed below as indicated by the arrows.

Learning Goal:

Students will understand the meaning of a parabola and demonstrate this knowledge by being able to graph the parabola and write the equation of the parabola graphed.

Don’t peek at the answers on the next

slide until you are finished!

Learning Goal:

Students will understand the meaning of a parabola and demonstrate this knowledge by being able to graph the parabola and write the equation of the parabola graphed.

Mat Activity:

Learning Goal:

Students will understand the meaning of a parabola and demonstrate this knowledge by being able to graph the parabola and write the equation of the parabola graphed.

Students should begin the worksheet. Any incomplete problems become the homework.

The next two slides are for optional practice.