1. Topic-
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| Graphing Quadratic Functions Through Technology |
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2. Content-
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| They review what are quadratic functions and then move to the functions
within the grid. The student will know what composes the Cartesian,
such as axes, origin, and points out of quadratic functions plane.
You will learn to solve quadratic formulas, such as factoring function
and formula of the square root functions. |
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3. Goals: Aims/Outcomes-
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1. The student will be able to use technology to solve graph functions.
2. The student will be able to display the functions in the coordinate
plane.
3. The student will be able to create a Cartesian plane and locate
points in the plane.
4. The student will be able to recognize the Cartesian plane axes.
5. The student will be able to solve quadratic functions without having
to make use of technology.
6. The student will know the FooPlot system for creating graphs. |
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4. Objectives-
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1.The student shows interest in the material being taught.
2. The student is interactive and critical.
3. The student demonstrates mastery over technology. |
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5. Materials and Aids-
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1. Using the FooPlot (available online) technological system.
2. Graphing Calculator.
3. Book grid and ruler. |
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6. Procedures/Methods-
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A. Introduction-
| It begins with a brief explanation of those who remember that they
are quadratic functions. Then it begins with an explanation of How
graphing quadratic functions? with an example on the board. And finally
How graphing quadratic functions? in FooPlot. The example to discuss
is traditionally discussed in this issue which is (x ^ 2 + 2x + 1
= 0). |
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B. Development-
Using the traditional example we have (x ^ 2 + 2x + 1 = 0) will
be equal to the factorization of (x + 1) ^ 2 = 0 and (x + 1) (x +
1) = 0. Then choose each bracket and equal to zero for the x-intercept,
then we have (x + 1) = 0 and (x + 1) = 0. However, we note that both
brackets have the same, in this case x + 1 , so we choose one parentheses.
We remove the parentheses and would have x + 1 = 0, now we solve for
the variable x, and we would have x = -1, the x-intercept is (-1,0).
Now look for the intercept, this occurs when x = 0, ie (0) ^ 2 + 2
(0) + 1 = 0 + 0 + 1 = 1, then the y-intercept is (0,1) of By what
we notice that the vertex of the function
(x ^ 2 + 2x + 1) = 0 is (-1,0) and (0,1) also we see that the coefficient
of x ^ 2 is positive, the function is increasing. After having the
information required draw the graph on graph paper and the FooPlot
system.
Now using the method of the quadratic formula in the year (x ^ 2-2x-1),
we know that a = 1, b = -2 and c = -1
(2 ± √ 〖(〖(- 2)〗 ^ 2-4 (1) (- 1))〗 ^) / (2 (1)) =
(2 ± √ 〖(4 + 4)〗 ^) / 2 =
(2 ± 〖〗 √8 ^) / 2 =
〖〗 ± √8 so we would like the x-intercept (-√8,0) and (√8,0).
In and,
(0) ^ 2-2 (0) -1 = 0 + 0-1 = -1, (0, -1. AL Like the previous example
that the function is increasing. After having the information required
draw the graph on graph paper and the FooPlot system. |
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C. Practice-
With the above explanation perform the following exercises.
Determine the intercept, the vertex of the graph, if the graph is
increasing or decreasing and build the graph.
A. Use the factorization
1. (4x ^ 2 - 12x + 9) = 0
2. (10x -21 -x ^ 2) = 0
3. (14x ^ 2 + 33xy + 18y ^ 2) = 0
B. Use the formula of the square root.
1. (- 3x ^ 2 - 5x + 9) = 0
2. (6x 2 + 7x - 11) = 0
3. (5x 12x ^ 2 + - 8) = 0 |
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D. Independent Practice-
The student will be able to acquire extra points by completing this
task.
Determine the intercept, the vertex of the graph, if the graph is
increasing or decreasing and build the graph.
1. (x ^ 2 + 3x + 2) = 0
2. (5x + -12X 28 ^ 2) = 0
3. (30x ^ 2 + 21x + 14) = 0.
4. (100x ^ 2 - 22x - 13) = 0.
5. (9x2 + 26x + 36) = 0.
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E. Accommodations (Differentiated Instruction)-
The student has a special task in which solves a quadratic equcaión
using their creativity. With this task is that the student is independent
on the task and explore the Internet to complete the task.
Here students can meet with the teacher in other hours you explain
the material you had any doubts. And students with special needs and
exceptional teacher tends to give a reasonable accommodation to the
student. |
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F. Checking for understanding-
Mentally solves these functions.
1. (x ^ 2 - 2x + 1) = 0
(x-1) ^ 2 = 0
x-1 = 0
x = 1
2. (4x 2 + 16x + 16) = 0.
4 (x ^ 2 + 4x + 4) = 0
4 (x + 2) ^ 2
+ x 2 = 0
x = -2
3. (3x ^ 2 - 10x - 8) = 0
(x - 4) (3x + 2) = 0
x - 4 = 0, or = 0 3x + 2
x = 4, or x = -2/3 |
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G. Closure-
| Quadratic functions help simplify polynomial functions for easy
to plot in the Cartesian plane. Admittedly, if the function we have
factored or else we will have to use the formula of the square root.
It is important to note that using quadratic functions can plot the
parables, find its intercept vertex. In the final minutes to finish
the class, students form a group, and the teacher begins to ask questions
about the material and the group context first gets a few extra points
in the daily class notes. |
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7. Evaluation-
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| El estudiante será evaluado por la participación que tenga en
clase. Tambien se evaluara por medio de la tarea diaria dentro del
salón de clases. Ademas sera evaluado si muestra dominio al utilizar
el sistema tecnolegico FooPolt. Y por medio de trabajos especiales
relacionados con el tema. |
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8. Teacher Reflection-
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| The child who shows interest in what is being taught acquires more
knowledge. Through this lesson, students learn what they are quadratic
functions, formulas and behavior that takes the parable. The teacher
will have 5 minutes to check student understanding about the material,
provided it is a smaller group of 25 students. |
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