"Image and Properties of Quadratic Functions" PPT courseware

Description

"Image and Properties of Quadratic Functions" PPT courseware

learning target

1. Be able to draw the image of y=ax²+k; y=a(x-h)², and be able to explore its properties based on the image.

2. Be able to flexibly apply the properties of y=ax²+k; y=a(x-h)² to solve related problems.

Review the past and learn the new:

The graph of the quadratic function y=x2 is ____, its opening is toward _____, and the vertex coordinate is _____; the axis of symmetry is ______, on the left side of the symmetry axis, y increases with the increase of x, in On the right side of the symmetry axis, y ______ as x increases. The function y=x2. When x=______, y has the most ______ value, and its most ______ value is ______.

Explore:

(1) What are the opening directions, symmetry axes, and vertices of parabolas y=x²+1 and y=x²-1?

Parabola y=x²+1: The opening is upward, the axis of symmetry is the y-axis, and the vertex is (0,1).

Parabola y=x²-1: the opening is upward, the axis of symmetry is the y-axis, and the vertex is (0,-1).

(2) The similarities and differences between parabola y=x²+1, y=x²-1 and parabola y=x²:

Similarities: ①Same shape and size

②The opening directions are the same

③The axes of symmetry are the same

Different points: The position of the vertex is different, and the position of the parabola is also different.

Thinking: If you translate the parabola y=2x²+1 upward by 5 units, which parabola will you get? What about moving it downward by 3.4 units?

(1) Get the parabola y=2x²+6

(2) Get the parabola y=2x²-2.4

knowledge consolidation

(1) The image of the function y=4x²+5 can be obtained by shifting the image of y=4x2 to ____ by ____ units; the image of y=4x²-11 can be obtained by moving the image of y=4x² to ____ Translate ____ units to get.

(2) Translate the image of the function y=-3x²+4 to ___ by ___ units to get the image of y=-3x²; translate the image of y=2x²-7 to ___ _ units get the image that can be obtained by y=2x². The image of y=x²+2 can be obtained by shifting the image of y=x²-7 toward ___ by ___ units.

(3) The opening ___ of the parabola y=-3x²+5, the symmetry axis is ___, the vertex coordinate is ___, on the left side of the symmetry axis, y increases with x, and ___ on the right side of the symmetry axis , y increases with the increase of x. When x=___, the maximum ___ value is obtained, which is equal to ___.

induction

Generally, parabola y=a(x-h)² has the following characteristics:

(1)The axis of symmetry is x=h;

(2)The vertex is (h,0).

(3) Parabola y=a(x-h)² can be obtained by translating parabola y=ax² to the left or right by |h|.

h>0, translate to the right;

h<0, translate left

practise

Draw the graph of the following function, and tell the opening direction, axis of symmetry, vertex of the parabola, what is the maximum or minimum value, and how is the increase or decrease? .

y=2(x-3)²

y=−2(x+3)²

y=−2(x-2)²

y=3(x+1)²

Expand and improve

1. After shifting the parabola y=ax² to the left, the abscissa coordinate of the vertex of the new parabola is -2, and the new parabola passes through the point (1,3), find the value of a.

2. Translate the parabola y=2x² left and right so that it intersects the x-axis at point A and the y-axis at point B. If the area of ​​△ABO is 8, find the analytical formula of the translated parabola.

(8). Find the analytical formula of the quadratic function according to the following requirements:

(1) It is known that the parabola y=ax²+c passes through the points (-3, 2) (0, -1) to find the analytical formula of the parabola line.

(2) The shape is the same as the image shape of y=-2x²+3, but the opening direction is different, and the vertex coordinate is the parabola analytical formula of (0, 1).

(3) The axis of symmetry is the y-axis, the vertical coordinate of the vertex is -3, and the analytical formula of the point passing through (1, 2),

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

"Image and Properties of Quadratic Functions" PPT courseware 3:

"The Image and Properties of Quadratic Functions" PPT Courseware 3 Observe the image and answer questions (1) What is the relationship between the image of the function y=3(x-1)2 and the image of y=3x2? Is it an axially symmetrical figure? ?What are its symmetry axis and vertex coordinates? (2) What values ​​does x take when the function y=3(x-1..

"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 (..

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Update Time: 2024-06-28

This template belongs to Mathematics courseware Qingdao Edition Ninth Grade Mathematics Volume 2 industry PPT template

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