MATH TEACHING SEQUENCE 1
Description of Activity:
was investigated in printed and electronic concepts of activity 1. His research verify how reliable are websites compared with those found in print. So they must take both the Internet literature as the book where you found it. ACTIVITY 1
Research on the Internet and compare it with some books concepts as
Function Function Types
quadratic function of a quadratic function Grafica
components of the graph of a quadratic function. ACTIVITY 2
Activity description examples will be proposed that involve different types of functions, in which students have to say whether or not involving a quadratic function. If it is to propose a way to solve it. At least they will have to take a stake in each proposal.
Problems
development activity leading to a quadratic function:
From a pedestrian bridge, with a height of 5.50 m, vertically dropped ball. How long will it take the ball hit the ground?
It uses a formula that relates the distance, time and gravity in this case is also a very important factor: d = ½ g t ² if we know that g = 9.81 m / sec ² and time t unknown.
A complete what is needed to reach a quadratic function. ________=
½__________ t ² if t = x
Transposing terms, the equation becomes:
_______x ²-_______= 0
The volume of a cylinder is 1000〗 〖cm ^ 3. Express the total area of \u200b\u200bthe cylinder as a function of the radio and make your graphic
extra Documents:
Video: "Application of the quadratic function" http://www.youtube.com/watch?v=TF2_IjxOtyY accessed August 13, 2010 . Activity 2
exercise involving quadratic functions. ACTIVITY 3
Activity description
The student conduct GeoGebra using graphs of a quadratic function and compare with other quadratic function, observe and perform their activity exercises 3. Then graph a quadratic function and a linear function, doing the exercises activity 4.
Development of activity
FINANCIAL ACTIVITY 3
GRAFICA of a quadratic function
in GeoGebra enter the data into the entrance area and draw the graph of y = x ², and answer the following questions:
In this case if we know the equation a quadratic function is given by y = ax ² + bx + c. What is the value of a? ________
The apex is at the point (_____,_____)
The socket is ________________ ________________
open branches
The axis of symmetry is x = __________
has a maximum or minimum value _______________
Now construct the graph of y = - x ², and answer: What is the
value of a? ___________
The apex is at the point (_____,_____)
The socket is ________________ ________________
open branches
The axis of symmetry is x = __________
has a maximum or minimum value
_______________ Make comments you have regarding the two graphs.
_________________________________________________________________________________________________________________________________________ determines the elements of the following quadratic functions with the help of GeoGebra:
f (x) = 2x ² + 8x -5
g (x) = x ² +4
h (x) =- x ² - 6x
k (x) = 3x ² + 1
f (x) = 3x ² + 9x + 1
FINANCIAL ACTIVITY 4
quadratic function FUNCTION LINEAR
in GeoGebra follow these graphics in a single Cartesian coordinate system:
1) y = x ² y = x (in input introduces first y = x ² the square you can put the bar after login, then y = x) using the spreadsheet performs the tables and graphs made separately to obtain the behavior of each table.
2) y = x ² +1 and y = x + 1 does the same as in the preceding paragraph.
now makes the observations on the behavior of each graph and the difference in each of the tables got.
Remarks Table 1 y = x ² y = x
______________________________________________________________________________________________________________________________________________
Observations Table 2 y = x ² + 1 y = x + 1
______________________________________________________________________________________________________________________________________________
ACTIVITY 5
Roots of quadratic equation in Association with the quadratic function
The graph of a quadratic function allows visually find the solution of the quadratic equation.
Using the worksheet get the table of values \u200b\u200band graph of the following quadratic functions:
f (x) = x ² + 2x -8
g (x) = x ² - 3x -10
Note that each graph intercepts the x axis at two points indicates the value of each point:
x_1 =__________ x_2 = __________ and __________ and
x_1 = x_2 =__________
These values \u200b\u200bare the roots or solutions of each of the previous quadratic functions. Using GeoGebra
determines the roots of the following quadratic functions and draw the roots in the graph.
f (x) = x ² + 3x -10 = ______ and x_2 x_1 =_______
g (x) = x ² + 2x +1 x_1 = x_2 = ______ and ______
h (x) = x ² - x - 30 x_1 = ______ and x_2 = ______
k (x) = x ² + 2x + 3 x_1 = ______ and x_2 = ______
f (x) = x ² + 2x - 3 x_1 = ______ and x_2 = ______
h (x ) = 0.5x ² - 6x x_1 = x_2 = ______ and ______
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