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"Image and Properties of Quadratic Functions" PPT Courseware 3
Observe images and answer questions
(1) What is the relationship between the graph of the function y=3(x-1)2 and the graph of y=3x2? Is it an axially symmetric graph? What are its symmetry axis and vertex coordinates?
(2) When x takes what values, the value of function y=3(x-1)2 increases with the increase of x value? When x takes what values, the value of function y=3(x-1)2 increases with the increase of x value. Decrease as x increases?
I think, I progress
Draw the graphs of the quadratic functions y=3x², y=3(x-1)2 and y=3(x-1)2+2 in the same coordinate system.
What is the relationship between the graphs of quadratic functions y=3x², y=3(x-1)2 and y=3(x-1)2+2? What are their opening directions, symmetry axes and vertex coordinates? What are the operations? Take a look at the picture.
Construct quadratic functions y=-3(x-1)2+2, y=-3(x-1)2-2, y=-3x² and y=-3(x-1)2 in the same coordinate system image
What is the relationship between the quadratic function y=-3(x-1)2+2 and the graph of y=-3(x-1)2-2 and y=-3x², y=-3(x-1)2 ?Are they axially symmetrical figures? What are its opening direction, axis of symmetry and vertex coordinates? When x takes what values, the value of y increases with the increase of x value? When x takes what values, y The value of decreases as the value of x increases?
The relationship between the quadratic function y=a(x-h)²+k and y=ax²
Generally, the image of the quadratic function y=a(x-h)²+k can be obtained from the image of y=ax²: the image of y=a(x-h)²+k(a≠0) can be regarded as y The image of =ax² is first translated left (right) by |h| units along the It is obtained by the entire upper (lower) translation of the axis by |k| units (when k>0, it translates upward; when k<0, it translates downward).
Therefore, the graph of the quadratic function y=a(x-h)²+k is a parabola, and its opening direction, axis of symmetry and vertex coordinates are related to the values of a, h, k.
The relationship between the quadratic function y=a(x-h)²+k and y=ax²
1. Similar points: (1) The shapes are the same (the images are all parabolas and the opening directions are the same).
(2) They are all axially symmetric figures.
(3) There is a maximum (large or small) value.
(4) When a>0, the opening is upward. On the left side of the symmetry axis, y decreases with the increase of x. On the right side of the symmetry axis, y increases with the increase of x. When a<0, With the opening downward, on the left side of the symmetry axis, y increases with the increase of x, and on the right side of the symmetry axis, y decreases with the increase of x.
2. Difference: Just the location is different
(1) The vertices are different: (h,k) and (0,0) respectively.
(2) The axes of symmetry are different: the straight line x = h and the y axis respectively.
(3) The maximum values are different: k and 0 respectively.
3. Connection: The image of y=a(x-h)²+k(a≠0) can be regarded as the image of y=ax². First, move the whole left (right) along the x-axis by |h| units (When h>0, translate to the right; when h<0, translate to the left), and then translate up (down) along the symmetry axis by |k| units (when k>0, translate upward ;When k<0, translate downward).
Keywords: teaching courseware on the image and properties of quadratic functions, Qingdao edition ninth grade mathematics volume 2 PPT courseware download, ninth grade mathematics slide courseware download, image and properties of quadratic functions PPT courseware download, .PPT format;
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