PhET/C2/Equation-Grapher/English

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Visual Cue Narration
Slide Number 1

Title Slide

Welcome to this tutorial on Equation Grapher.
Slide Number 2

Learning Objectives

We will demonstrate PhET simulation,

Equation Grapher

In this tutorial, we will demonstrate Equation Grapher PhET simulation.
Slide Number 3

System Requirements

Ubuntu Linux OS version 16.04

Java version 1.8.0

Firefox Web Browser 60.0.02

Here I am using,

Ubuntu Linux OS version 16.04

Java version 1.8.0

Firefox Web Browser version 60.0.02

Slide Number 4

Pre-requisites

Learner should be familiar with topics in high school mathematics.
Slide Number 5

Learning Goals

Lines y = bx + c and y = c

Quadratic polynomials y = ax2 + bx + c.

Using this simulation we will look at,

Lines of the form y = bx + c and y = c

Quadratic polynomials y equals ax squared plus bx plus c

Slide Number 6

Binomial Theorem

Binomial theorem states that if a, b ∈ ℝ, index n is a positive integer, 0 ≤ r ≤n, then,

(a + b)n = nC0 an + nC1 an-1 b1 + nC2 an-2 b2 + … + nCr an-r br + … + nCn bn

Reminder: nC1 = n!/[1! (n-1)!]

Binomial Theorem

a and b are real numbers, index n is a positive integer.

r lies between 0 and n.

Then, Binomial theorem states that a plus b raised to n can be expanded as shown.

Slide Number 7

Link for PhET simulation

http://phet.colorado.edu

Use the given link to download the simulation.

http://phet.colorado.edu

I have already downloaded Equation Grapher simulation to my Downloads folder.
Press Ctrl+Alt+T to open the terminal.

Type cd Downloads >> press Enter.

Type java space hyphen jar space equation-grapher_en.jar.

Point to the opened file format.

To open the jar file, open the terminal.

At the terminal prompt, type cd Downloads and press Enter.

Type java space hyphen jar space equation-grapher_en.jar.

Press Enter.

File opens in the browser in html format.

Cursor on the interface. This is the interface for the Equation Grapher simulation.
Point to the interface. The interface shows Cartesian co-ordinate system of x and y axes.
Point to the first quadrant.

Point to the quadratic function, y = ax2 + bx + c.

Point to the sliders and display boxes.

Point to the red Zero button.

Point to the green Save button.

Point to the equation.

The first quadrant contains:

The red-colored quadratic equation, y equals ax squared plus bx plus c

Three sliders and display boxes under ax2, bx and c

The sliders allow you to change the values of the coefficients, a, b and c.

The display boxes show these values and can be used to enter values.

A red Zero button to set all sliders at 0

A green Save button to save the equation

The updated equation in red is shown below the sliders.

Point to the fourth quadrant.

Point to the quadratic equation.

Point to the check boxes.

Point to the violet, green and blue terms.

The fourth quadrant contains the

Quadratic equation y = ax2+bx+c

Three check boxes under ax2, bx and c

Note that the ax squared term is violet, bx is green and c is blue.

In the first quadrant, in the display box below ax2, type 1.

Point to the slider under ax2.

In the first quadrant, in the display box below ax squared, type 1.

Observe how the slider under ax squared also moves to 1.

Point to the red parabola and origin (0,0). A red parabola with vertex at origin 0 comma 0 appears in the window.

It opens upwards.

In the first quadrant, in the display box below bx, type 1 In the first quadrant, in the display box below bx, type 1.
Point to the parabola. Observe how the parabola shifts downwards and to the left.
In the first quadrant, in the display box below c, type 1. In the first quadrant, in the display box below c, type 1.
Point to the parabola. Observe how the parabola moves upwards.
In the fourth quadrant, check the box below the violet coloured ax2 term. In the fourth quadrant, check the box below the violet coloured ax squared term.
Point to the violet and red parabolas.

Point to the equation.

A violet parabola appears next to the red parabola.

This violet parabola corresponds to the y equals ax squared part of the red equation.

Point to the equation, y = x2, in the first quadrant. The equation for the violet parabola is y equals x squared.
Check the box below the green bx term in the fourth quadrant. Now, in the fourth quadrant, check the box below the green bx term.
Point to the green line.

Point to the origin (0,0).

Point to the equation, y = x, in the first quadrant.

Observe how a green line appears in the Cartesian plane.

It passes through the origin 0 comma 0.

It corresponds to the x term and its equation is y equals x.

Check the box below the blue c term in the fourth quadrant. Now, in the fourth quadrant,check the box below the blue c term .
Point to the blue line.

Point to the equation, y=c.

Observe how a blue line appears in the Cartesian plane.

Its equation is y equals c and it corresponds to the constant term of the equation.

Click on the green Save button. Click on the green Save button.
Point to the blue saved parabola, y = x2+ x + 1. This saves the equation y equals x squared plus x plus 1.
Change values for a, band c.

Point to the sliders and the display boxes below the terms.

Point to the graphs.

Change the values for a, b and c.

You can either use the sliders or type in the display boxes below the terms.

Observe the effects of these changes on the graphs.

Point to the blue saved parabola, y = x2 + x + 1. Note that as you change a, b and c, you can still see the parabola y equals x squared plus x plus 1.

This is because we saved this equation.

Save other graphs that you want to compare to see the effects of a, b and c.

You can only save one equation at a time.

Point to the blue Erase button. Note that after you have saved an equation, a blue Erase button appears.

This will erase the saved equation.

Click on the red Zero button. Click on the red Zero button.

This resets all coefficients a, b and c to 0.

Slide Number 8

Assignment

As an assignment, compare the parabolas graphed for different combinations of:

a <0 and a >0

b <0 and b >0

c <0 and c >0

Slide Number 9

Summary

In this tutorial, we have demonstrated the

Equation Grapher PhET simulation

Slide Number 10

Summary

Using this simulation, we have looked at:

Lines of the form y = bx + c and y = c

Quadratic polynomials y = ax2 + bx + c

Slide Number 11

About the Spoken Tutorial Project

Watch the video available at http://spoken-tutorial.org/ What_is_a_Spoken_Tutorial

It summarizes the Spoken Tutorial project

If you do not have good bandwidth, you can download and watch it

The video at the following link summarizes the Spoken Tutorial project.

Please download and watch it

Slide Number 12

Spoken Tutorial workshops

The Spoken Tutorial Project team conducts workshops using spoken tutorials and gives certificates on passing online tests.

For more details, please write to us.

Slide Number 13

Forum for specific questions:

Do you have questions in THIS Spoken Tutorial?

Please visit this site

Choose the minute and second where you have the question

Explain your question briefly

Someone from our team will answer them

Please post your timed queries in this forum.
Slide Number 14

Acknowledgement

This project is partially funded by Pandit Madan Mohan Malaviya National Mission on Teachers and Teaching
Slide Number 15

Acknowledgement

Spoken Tutorial Project is funded by NMEICT, MHRD, Government of India.

More information on this mission is available at this link.

This is Vidhya Iyer from IIT Bombay signing off.

Thank you for joining.

Contributors and Content Editors

Madhurig, Vidhya

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