Taking the function y= 1/x as an example, this paper explains how to show the symmetry of quadratic function y=x2 and function y= 1/x by using the geometric sketchpad animation.
1, "drawing"-"drawing a new function", drawing y =1/x;
2. Make a straight line y =-x; (You can't draw an image. Choose the origin and point (1,-1) to construct a straight line. )
3. Draw a movable point A on a straight line, select the movable point A and the straight line to make a vertical line;
4. Construct two intersection points b and c between the straight line and the image of y= 1/x;
5. Measure the distances between point A and point B, point A and point C, and the measured values should be as close as possible;
6. By dragging point A on a straight line, we can intuitively observe that the distances from point B and point C to the symmetry axis are always equal, and the straight line BC is perpendicular to the symmetry axis.
How to make quadratic function image courseware 1 with geometry sketchpad, drawing-drawing new function-inputting analytic function.
2. You can create three parameters and use them to create a parameter parsing function (or draw a new function) in the new function. Changing parameters can change the graph.
How to dynamically demonstrate the image of quadratic function 1 with geometric sketchpad and quickly make the image of quadratic function we want; 2. Dynamically demonstrate several forms of images of quadratic function to help students understand the images and properties of quadratic function and the translation and symmetry relationship between several forms of images of quadratic function; 3. Dynamically demonstrate that the function value of quadratic function changes with the change of independent variables.
What kind of dynamic translation and folding is needed? It varies from point to point.
How to make quadratic function diagram with geometric sketchpad? Quadratic function is a mathematical model to describe the law of movement change in the objective world, and it is an important mathematical concept based on change and correspondence. In order to make students understand the interdependence between variables of quadratic function and clearly see the translation and symmetry among several forms of quadratic function, such as y=ax2, y=ax2 +k, Y = (X-H) 2, Y = A (X-H) 2+K, y=ax2+bx+c, it is necessary to provide students with a lot of image materials. Of course, it is best to let them intuitively watch how the graph changes when several parameters A, B, C or parameters H and K in the function change, and see the corresponding relationship of variables in the process of motion change.
How to make quadratic function diagram with geometric sketchpad
Quadratic function is a mathematical model to describe the law of movement change in the objective world, and it is an important mathematical program based on change and correspondence.
Reading. Let students understand the interdependence between variables of quadratic function and clearly see several forms of quadratic function.
y=ax2
、
y=ax2
+k
、
y=
(
x
-
h
)
2
、
y=a
(
x
-
h
)
2+k
、
y=ax2+bx+c
Translation and symmetry between them,
It is necessary to provide students with a large number of image materials.
Let the students observe,
Analysis and comparison.
Of course, it is best to let them see it intuitively.
Look at several parameters in the function.
a
、
b
、
c
Or parameters
h
、
k
How does the graph change when it changes? Look at it moving.
And the corresponding relationship between variables in the process of change.
This was explained orally by the teacher.
It is difficult to achieve this goal by drawing on the blackboard.
The use of multimedia technology can help us do this.
Geometric sketchpad and
Z+Z
Educational platform can make abstract function problems intuitive and vivid, and change static into dynamic and dynamic performance.
Display the drawing process,
Dynamically demonstrate the change of function values with independent variables,
Help students understand the concept of function,
Images and attributes. How to effectively integrate information technology with mathematics teaching? How to connect the geometric sketchpad with
Z+Z
educational level
These new teaching tools are perfectly integrated into the teaching process of quadratic function? Let me briefly introduce how to draw with geometry.
Making quadratic function courseware with wooden boards;
I want to make courseware with geometry sketchpad, and there are three main goals:
1
And quickly make the quadratic function we want.
Image;
2
Dynamically demonstrate several forms of images of quadratic function to help students understand the images, properties and functions of quadratic function.
Translation and symmetry of two kinds of quadratic function images;
three
Dynamic demonstration of function value of quadratic function of independent variable
The changing scene helps students understand the monotonicity and extreme value of quadratic function.
Firstly, the geometric sketchpad is used as a quadratic function.
y=3x2
-
4x+ 1
Image of. This form of image is easier to use in several places.
Draw on the drawing board window. Teachers can improvise in class.
1
Establish a plane rectangular coordinate system. After entering the Geometry Sketchpad window, click the Edit window.
"
drawing
"
choose
"
show
Coordinate axis
"
,
At this point, you can see a coordinate axis appear on the window.
You pull
x
The sliding point on the positive semi-axis of the shaft,
You can change the size of the unit length.
2
Draw some. Click the Point Drawing Tool in the toolbar on the left side of the editing window.
, at
x
Click anywhere on the axis to click.
x
Make a point on the axis, such as a dot.
A
. If you want to change this point to another name, you can use the hand tool.
,
Double-click the letter
A
Enter the required letters in the dialog box that appears.
three
, measure the coordinates. Click the point.
A
, click the edit window.
"
Measurement and calculation
"
, select
"
coordinate
"
, you can see the editing window.
Point out in the upper left corner of the mouth.
A
Coordinates of
, for example
A(-2. 18，0.00)
four
、
Separate coordinates.
Release coordinate
A
The abscissa in is separated,
As a quadratic function
y=3x2
-
4x+ 1
Independent variable of
x
.
Double-click a point in the editing window.
A
Coordinates of
(-2. 18,0.00)
A calculator will appear,
Then click the calculator.
"
value
"
,
Then select a point.
A
In the drop-down menu
x
, and then press OK, that's all.
A
The abscissa of
XA=-2. 18
lone
How to use the geometric sketchpad, a powerful tool in mathematics, is first embodied in the making of various function diagrams. Let's take the quadratic function diagram as an example to talk about the use of the geometric sketchpad. Specific steps: 1. Create a new drawing, select "Chart" in the menu bar, and click "Build Axis". 2. Select the "Draw Point" tool in the toolbar, and the mouse pointer will turn into a cross. Click on the horizontal axis of the coordinate axis to draw a point, make sure that the point is selected, and select "Mark Text &; Label tool, click on the point just drawn, and the "label" of the point will be displayed (assuming "C"). Make sure that point C is selected, select "Measure" in the menu bar, and click "Coordinate" to get the coordinates of point C. 3. Select "Select &; Translation tool: click the coordinates of point C to make it selected, then select Measure in the menu bar, click Calculate … to open the calculator window, click the numerical button, put the mouse on point C, select X, and click OK in the calculator window, so that we can drag point C with the mouse, and we will find that the measurement of its abscissa will change accordingly. 4. Let's tidy up the interface a little, click the coordinates of point C with the mouse to make it in the selected state, then press ctrl and H keys at the same time to hide the coordinates of point C .. and then select "Tag text &; Label tool, double-click the measured value on the abscissa of point C with the mouse, and select the text format in the measurement format window that appears, and two text boxes will appear. Change "x[c]=" in the text box on the left to "x=", and then press "OK" in the Measurement Format window. After the above work, we have constructed the independent variable of quadratic function. Let's construct the coefficients a, b and c of quadratic function. The construction processes of coefficients A, B and C are exactly the same. We only introduce the construction process of coefficient A in detail. 5. Select the "Draw Point" tool in the toolbar, draw a point on the horizontal axis of the coordinate axis, and select "Mark Text & Label tool, click on the point just drawn, and the "label" of the point will be displayed (assuming "D"). Then select the "Select &" translation button, hold down the shift key, and click the horizontal axis of the coordinate axis with the mouse, so that the D point and the horizontal axis of the coordinate axis are selected at the same time (if you want to select multiple objects, hold down the shift key first, and then use the mouse to select. If you want to cancel the selection of an object, just click it again with the mouse), select "Drawing" in the menu bar and click "Vertical Line", and a straight line perpendicular to the horizontal axis of the coordinate axis and passing through point D will be drawn. Draw a point on this straight line and select "Mark Text &; Label tool. Click on the point just drawn, and the label of the point will be displayed (assuming "E"). Double-click the label of the point (letter "E"), change the "E" to "A" in the displayed Reset Label window, and press the "OK" button in the Reset Label window. Then select "Select &" in the toolbar. Pan tool, click the line you just drew, and then press ctrl and H to hide the line at the same time. Select point A, select "Measure" in the menu bar, click "Coordinate" to get the coordinates of point A ... Select the coordinates of point A, select "Measure" in the menu bar, click "Calculate …" to open the calculator window, click the "Value" button with the mouse, put the mouse on "Point A", select Y, and then click "OK" button in the calculator window, and so on. 6. Let's tidy up the interface a little bit, hide the coordinates of point A, and select "Tag Text &; Label tool, double-click the measured value of the ordinate of point A with the mouse, select the text format in the measurement format window that appears, and two text boxes will appear. Change "y[a]=" in the text box on the left to "a=" and press the "OK" button in the measurement format window. Then select "Select &; Pan button, hold down the shift key, click point A and point D with the mouse, so that point A and point D are selected at the same time, select drawing in the menu bar, and click the line segment with the mouse. 7. We can construct the coefficients b and c by repeating steps 5 and 6. 8. Select "Select &; Shift key, hold down the Shift key, click the measured values X, A, B, C (make sure that no other objects are selected), select measurement in the menu bar, click Calculate …, click the numerical button in the calculator window that appears, select A, click the * button, and click. Click the+button, click the numerical button and select B, click the * button, click the numerical button and select X, click the+button, click the numerical button and select C, and finally press the OK button to obtain a new measured value. Select Tag Text &; In the toolbar. Label tool, double-click the just-obtained measurement value with the mouse to open the measurement value format window, change "a * x 2+b * x+c =" in the left text box to "y=", and press the "OK" button in the measurement value format window. 9. Select "Select &; Translation tool, hold down the shift key, click the measured values X and Y (pay attention to the order), select Chart in the menu bar, click Draw (x, y) to construct a new point (if the point does not appear on the screen, you can make it visible by changing the positions of point C, point A, point B and point C), and select "Make it visible" in the toolbar. Label tool, click the point just constructed with the mouse, and its label (assuming "J") will be displayed. Hold down the shift key, select point J and point C, and select "Drawing" in the menu bar. After clicking "Trajectory", the image of quadratic function will appear on the screen. You can try to drag points A, B and C to observe the change of quadratic function image. If the image is not smooth, you can select "Display" in the menu bar and then click "Parameter Settings". In the object parameter selection window that appears, click the "Other …" button to open the "Advanced Parameter Selection" window and set the number of samples on the track to 100 (the maximum value is 99). The higher the value, the smoother the image will be, but the computer will be slower), press the Continue button in the Advanced Parameter Selection window, then press the OK button in the Object Parameter Selection window, and then rebuild the trajectory. 10. Let's beautify the interface a little. You can hide points C and J, or labels D, F and H. Select the image of quadratic function, click the right mouse button, and set its line type as thick line and its color as red.
How to draw a quadratic function diagram with the geometric sketchpad —— Draw a new function: 5 * x 2+3 * x-1.