"Graphic of Quadratic Function y=ax2+bx+c" Quadratic Function PPT Courseware

Description

"Graphic of Quadratic Function y=ax2+bx+c" Quadratic Function PPT Courseware

learning target

1. Be able to draw the image of y=ax²+bx+c;

2. Understand the properties of y=ax²+bx+c;

3. Master the connection and difference between the images and properties of y=ax²+bx+c and y=a(x-h)²+k.

New course introduction

Tell us the opening direction, axis of symmetry, and vertex coordinates of the image of the quadratic function y=-4(x-2)²+1. How is it obtained by translation of y=-4x²?

We know that to draw the graph of the quadratic function y=3x², by translating the parabola y=3x² we can get the graph of the quadratic function y=3x²-6x+5.

How to directly draw the graph of the function y=3x²-6x+5?

Can you convert the function y=ax²+bx+c into a vertex form through the collocation method?

Generally, for the quadratic function y=ax²+bx+c, we can use the matching method to deduce its symmetry axis and vertex coordinates.

Extract quadratic term coefficients

Recipe: plus and minus the square of half the absolute value of the coefficient of the first term

Organize: convert the first three terms into square form, and merge the last two terms into similar terms

Determine the symmetry axis and vertex coordinates of the following quadratic function graph according to the formula:

(1)y=2x²-12x+13

The axis of symmetry is x=3, and the vertex coordinate is (3,-5)

(2)y=-5x²+80x-319

The axis of symmetry is x=8, and the vertex coordinate is (8,1)

(3)y=3(x+2)(2-x)

The axis of symmetry is x=0, and the vertex coordinate is (0,12)

The relationship between the quadratic function y=ax²+bx+c(a≠0) 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) all have maximum (or minimum) values.

(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. Differences:

(1) The positions are different (2) The vertices are different: _________ and (0,0) respectively.

(3) The axes of symmetry are different: __________ and y-axis respectively.

(4) The maximum values ​​are different: _______ 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 |____| units (When ___>0, translate to the right; when ___ <0, translate to the left), and then translate up (down) along the symmetry axis by |_____| units

(When ______>0, translate upward; when _____<0, translate downward).

Practice in class

1. (Wuzhou High School Entrance Examination) It is known that the graph of the quadratic function y=ax²+bx+c is as shown in the figure, then which of the following judgments is incorrect ( )

A. ac<0

B． a-b+c>0

C. b=-4a

D. The roots of the equation ax²+bx+c=0 about x are x1=-1,x2=5

2. (Zhaotong High School Entrance Examination) The graph of the quadratic function y=ax²+bx+c is as shown in the figure, then the following conclusion is correct ( )

A. a<0, b<0, c>0, b2-4ac>0

B． a>0, b<0, c>0, b2-4ac<0

C. a<0, b>0, c<0, b2-4ac>0

D. a<0, b>0, c>0, b2-4ac>0

3． (Panzhihua High School Entrance Examination) As shown in the figure, the approximate image of the quadratic function y=ax²-bx+2 is as shown in the figure, then the image of the function y=-ax+b does not pass through ( )

A. Quadrant 1

B． second quadrant

C. Quadrant 3

D. Quadrant 4

Summary of this lesson

1. Be able to skillfully find the maximum value of a quadratic function, and be able to judge the increase or decrease of a function within a certain range based on its properties.

2. Able to determine the relational expression, vertex coordinates, and axis of symmetry of a quadratic function based on conditions.

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"Graphic of Quadratic Function y=ax2+bx+c" Quadratic Function PPT Courseware 4:

"Graphic of Quadratic Function y=ax2+bx+c" Quadratic Function PPT Courseware 4 Knowledge Review: Generally, the parabola y=a(x-h)p+k has the same shape as y=ax, but the position is different y=ax Add up and subtract down/Add left and subtract right y=a(x-h)+k Parabola y=a(x-h)2+k has the following characteristics: 1..

"Graphic of Quadratic Function y=ax2+bx+c" Quadratic Function PPT Courseware 3:

"Graphic of Quadratic Function y=ax2+bx+c" Quadratic Function PPT Courseware 3 Knowledge Review: Generally, the parabola y=a(x-h)2+k has the same shape as y=ax2, but the position is different y=ax2 ---y=a(x-h)2+k The image and properties of parabola y=a(x-h)2+k: 1. When a�0..

"Graphic of Quadratic Function y=ax2+bx+c" Quadratic Function PPT Courseware 2:

"The Graph of the Quadratic Function y=ax2+bx+c" Quadratic Function PPT Courseware 2 Learning Objectives 1. Experience the process of exploring the methods and properties of the graph of the quadratic function y=ax2+bx+c. 2. Experience The necessity of establishing the symmetry axis and vertex coordinate formulas of quadratic functions. 3. Be able to make y=a..

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Update Time: 2024-10-04

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