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# Artifact3 allen

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### Artifact3 allen

1. 1. 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. 2. 2. I noticed while I varied the value of (b) the parabola translated along the (c) value.
3. 3. 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.
4. 4. 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)
5. 5. 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.
6. 6. 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.
7. 7. IDP TPACK TEMPLATE (INSTRUCTIONAL DESIGN PROJECT TEMPLATE) NAME: ___Thomas Allen_____ DATE:____12/4/12_____ Describe: content here. Content. (COMMON CORE 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.★ Describe:Standards of mathematical Practice Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Use appropriate tools strategically 1. Attend to precision. Pedagogy. Pedagogy includes both what the teacher does and what the student does. It includes where, what, and how learning takes place. It is about what works best for a particular content with the needs of the learner. Look for and express regularity in repeated reasoning. 1. Describe instructional strategy (method) appropriate for the content, the learning environment, and students. This is what the teacher will plan and implement. This lesson will be exploration based. The teacher will go over the basic topics such as the standard form of an equation and the basic techniques that manipulate said equation with use of TI-Inspire Additionally the teacher will present the class with an appropriate worksheet to guide the students along. Walk around the class during the student’s investigation and ask any probing questions. 2. Describe what learner will be able to do, say, write, calculate, or solve as the learning objective. This is what the student does. The student will be able to explore transformations in the quadratic equation based on the varying coefficients byutilizingsliders as well as using multiple functions and their graphs on the same plane in order to gain an understanding of each coefficient and its respective effect on the graph. 3. Describe how creative thinking--or, critical thinking, --or innovative problem solving is reflected in the content. In this lesson the sliders will help show what the effects that each coefficient has on its function but will not give an explicit answer as to why. This implores the student to discretely figure out what is going on with the function in relation to its varying coefficients.