Thomas Allen Dr. Adu-Gyamfi 12/4/13 Artifact 3 This artifact is about using Ti-Nspire software to help demonstrate the translations that a quadratic function moves through depending on which value is replaced as a variable. We also see how a quadratic function keeps it’s the parameter where the roots stay 3 and 5 while the function is being manipulated by outside factor. 1. I noticed while I varied the value of (a) the slope of the parabola locus varied along with the value of the variable (a).
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Thomas Allen
Dr. Adu-Gyamfi
12/4/13
Artifact 3
This artifact is about using Ti-Nspire software to help demonstrate the translations that a quadratic
function moves through depending on which value is replaced as a variable. We also see how a
quadratic function keeps it’s the parameter where the roots stay 3 and 5 while the function is being
manipulated by outside factor.
1. I noticed while I varied the value of (a) the slope of the parabola locus varied along with the
value of the variable (a).
2. I noticed while I varied the value of (b) the parabola translated along the (c) value.
3. I noticed while I varied the value of (c) the parabola translated up and down according to the
value of (c).
A) What happens to the graph as a varies and b and c are held constant?
When a varies from negative to positive the direction of the parabola switches from downward
to upward.
B) Is there a common point to all the graphs? What is it?
There is a common point is at 3 which is the constant for variable c in the function
a*x^(2)+2*x+3
C) What is the significance of the graph where a=0?
When a is zero the expression losses a degree and transforms into a linear function.
A) What happens to the graph as b varies and a and c are held constant?
The graph translates across the c variable constant 3.
B) Is there a common point to all the graphs? What is it?
Yes the c variable which took the value of 3 in the function x^(2)+b*x+3.
C) What is the significance of the graph where b=0?
When b is equal to zero the reflection point of the function x^(2)+b*x+3 lies on the y axis and
intersects at point (0,3)
A) What happens to the graph as c varies and a and b are held constant?
The function x^(2)+2*x+c translates upward and downward according to the varying c variable.
B) Is there a common point to all the graphs? What is it?
There is no common point of all the graphs share with respect to intersection points.
C) What is the significance of the graph where c=0?
When c is equal to 0 the y coordinate lies on the x-axis.
1. What do you notice about the roots of all 15 graphs? The roots stay the same as long as the constants 3 and 5 are not altered by a computation due to the order of operations.
2. What do you notice about the intercepts of these graphs? All of the intercepts are through x coordinates (3,0) and (5,0) with the exception of when a is equal to 0 of the function (x-3)*(x-5)*a
3. What do you notice about the intersection points. The points are all through x values 3 and 5.
4. What do you notice about the Orientation or Position of the graphs. The graphs are all scalar multiples of each other and as the variable a varies from negative to positive the orientation of the graphs switch from opening downward to upward.
5. Do they have common points? What can you say about their common points. They have the points (3,0) and (5,0) in common.
6. What do you notice about the correlation between the orientation of the graphs and the sign or coefficient of the x^2 term.
The orientation of the graph opens upward when the value of the coefficient of the x^2 is positive and it opens downward when it takes on a negative value.
7. What do you notice about the locus of the vertex of each of these graphs? The locus of the vertex lies on the axis of symmetry.
TI-Inspire isa computer software that combinesvarious elements of mathematics
that enables its user to gain a deep conceptual understanding of the properties and
concepts in question. As in this case the relationship between algebraic and
graphical representations of quadratic functions.
2. Describe how the technology enhances the lesson, transforms
content, and/or supports pedagogy.
This technology in this lesson enables the students to manipulatethevarious
coefficient values. They can easily manipulate the coefficient value and receive an
instant image that represents the change that was made to the function as opposed to
having to graph each graph individually. This also allows the students to quickly
make and test conjectures about the changes made to the function. The geometry
trace function in TI-Inspire is also useful in that it will allow the user to trace a
certain point of the graph and show its translation over the plane according to the
changes made to the function.
3. Describe how the technology affects student’s thinking processes.
Tracing the vertex of the quadratic equations the students will be able to create a
conjecture about how each of the coefficients makes divers transformationsto the
parabola. This application is useful in that it shows the previous changes to the
quadratic equation.
Reflect—how did the lesson
activity fit the content? How did the
technology enhance both the content
and the lesson activity?
Reflection
The lesson reflects what the content was based which was the common core
standards.Students weren’t necessarily picking out different pieces of the graph but
they are using those pieces to create an understanding of the transformations of the
quadratic equation. The technology made it feasible to put a plethora of graphs on
one graph and be able to look at them at once and see the change according to the
changes made to the respective variable.
Lesson Plan Template MATE 4001 (2013)
Title: Quadratic Transformations
Subject Area: Math 2
Grade Level: Secondary
Concept/Topic to teach: Transformationsof Quadratics
Learning Objectives:
Content objectives (students will be able to……….) Know each coefficients effect on the graph and how they interact with each other.
Essential Question
What question should student be able to answer as a result of completing this lesson?
What are the effects of the variables (a), (b),and (c) on the quadratic equation
and its graph?
Standards addressed:
Common Core State Mathematics Standards:
CCSS.Math.Content.HSF-IF.C.7 Graph functions expressed symbolically and show key features of the
graph, by hand in simple cases and using technology for more complicated cases.★
Common Core State Mathematical Practice Standards:
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Use appropriate tools strategically
Attend to precision.
Look for and express regularity in repeated reasoning.
Technology Standards: HS.TT.1.1:Use appropriate technology tools and other resources to access information (multi-database search engines, online primary resources, virtual interviews with content experts).
HS.TT.1.2:Use appropriate technology tools and other resources to organize information (e.g. online note-taking tools, collaborative wikis).
Required Materials:
Computers, Paper /Pencil, Projector
Notes to the reader:
Students already have a basic knowledge of the quadratic function, and how to use TI-Inspire.