"Image and Properties of Quadratic Functions" PPT Courseware 3

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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;

For more information about the "Graphics and Properties of Quadratic Functions" PPT courseware, please click on the "Graphics and Properties of Quadratic Functions" PPT tab.

"Image and Properties of Quadratic Functions" PPT courseware 2:

"The Image and Properties of Quadratic Functions" PPT Courseware 2 Review Objectives: 1. Review and master the images and properties of quadratic functions. 2. Be proficient in finding the analytical expression of quadratic functions. 3. Master the relationship between quadratic functions, quadratic equations of one variable and quadratic inequalities of one variable. Warm up before class (..

"Graphics and Properties of Quadratic Functions" PPT courseware:

"Images and Properties of Quadratic Functions" PPT courseware Learning objectives 1. Be able to draw the image of y=ax+k; y=a(x-h), and explore its properties based on the image. 2. Be able to flexibly apply the properties of y=ax+k; y=a(x-h) to solve related problems. Review the past and learn the new: Second letter...

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Update Time: 2024-09-08

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