"Image and Properties of Quadratic Functions" PPT

Description

"Image and Properties of Quadratic Functions" PPT

Part One: Knowledge Review:

1. The image and properties of parabola y=a(x-h)2+k:

1. When a�0, open _______,

When a�0, the opening _______,

2.The axis of symmetry is_______;

3.The coordinates of the vertex are _______.

2. Generally, the ______ of parabola y=a(x-h)2+k and y=ax2 are the same, but ______ are different

The image and properties of quadratic functions PPT, part 2 content: exploration:

Generally, we can use the matching method to find the vertex and axis of symmetry of the parabola y=ax2+bx+c(a≠0).

y=ax2+bx+c

in conclusion

1. The vertex coordinates of the image of function y= ax2+bx+c:

Axis of symmetry: straight line

Example 2 Find the symmetry axis and vertex coordinates of the parabola y=x2+2x-1, and draw its image.

Solution: ∵y=x2+2x-1=(x+1)2-2,

∴The axis of symmetry of the parabola is x=-1, and the vertex coordinates are (-1, -2).

(1) List:

(2) In the rectangular coordinate system, draw points and connect lines to get the image of the quadratic function y=x2+2x-1, as shown in Figure 30-2-7.

Example 3 Determine the expression of the parabola according to the following conditions.

(1) The vertex coordinates of the parabola y=-2x2+px+q are (-3, 5).

(2) Parabola y=ax2+bx-6 passes through points A (-1, 3) and B (2, -6).

Graphics and properties of quadratic functions PPT, part 3: exercises:

1. The coordinates of the intersection point of the parabola y=4x2-11x-3 and the y-axis are ______; the coordinates of the intersection point of the parabola y=4x2-11x-3 and the x-axis are ______;

2. The coordinates of the intersection point of the parabola y=-6x2-x+2 and the y-axis are ______; the coordinates of the intersection point of the parabola y=-6x2-x+2 and the x-axis are ______;

think

How to draw the graph of function y= ax2+bx+c?

Notice

When drawing points of the image of a quadratic function, first determine the vertex, and then symmetrically select the same number of points on both sides of the vertex. Generally, 5-7 points are enough.

Keywords: Free download of mathematics PPT courseware for the second volume of the ninth grade of Hebei Education Edition, PPT download of images and properties of quadratic functions, .PPT format;

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

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Update Time: 2024-06-20

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

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