"Getting to Know Parabolas" Quadratic Function PPT Courseware 2

Description

"Getting to Know Parabolas" Quadratic Function PPT Courseware 2

learning target

1. Be able to use the point drawing method to draw the graphs of quadratic functions y=x2 and y=-x2;

2. Based on the graphs of functions y=x2 and y=-x2, intuitively understand its properties.

Read textbook P41----P42 and think:

1. Can you use the point tracing method to draw the graph of the quadratic function y=x2?

2. Can you combine the image of the quadratic function y=x2 and talk about its related properties?

Self-study test

(1) What is the shape of the graph of the quadratic function y=-x2?

(2) Think about it first, and then make an image of it.

(3) What is its relationship with the graph of the quadratic function y=x2?

Appreciation of examples

1. It is known that the parabola y=ax2 passes through point A (-2, -8).

(1) Find the functional analytical formula of this parabola;

(2) Determine whether point B (-1, - 4) is on this parabola.

(3) Find the coordinates of the point on the parabola whose ordinate is -6.

Solution (1) Substituting (-2, -8) into y=ax2, we get -8=a(-2)2,

The solution is a= -2, and the analytical formula of the function is y= -2x2.

(2) Substituting x=-1, y=-2≠-4. So point B is not on the parabola.

(3) From -6=-2x2, we get x2=3, x=±√3

So there are two points with the ordinate of -6, they are (√3,-6) and (-√3,-6)

Self-study test

1. The graphs of function y=ax² (a≠0) and function y=kx-2 intersect at point A (-1, -1).

2. A certain culvert is parabolic. Its cross-section is as shown in the figure. The measured width of the water surface is AB=1.6m, and the distance from the vertex O of the culvert to the water surface is 2.4m. In the rectangular coordinate system in the figure, find the expression of the parabola where the culvert is located.

3. The shape of a parabolic arch bridge can be described by y=-x²

1) When the distance from the water surface to the top of the bridge arch is 2 meters, how many meters is the width of the water surface?

2) When the water surface is 4 meters wide, how many meters is the distance from the water surface to the top of the bridge arch?

4. It is known that the image of the quadratic function y=ax2 intersects the straight line y=2x+3 at (3, b)

(1) Find the values ​​of a and b

(2) Determine the opening direction of the image with y=ax2, and tell the symmetry axis, vertex coordinates of this parabola and how the value of y changes as the value of x increases when x>0.

(3) Suppose the intersection points of the straight line y=2x+3 and the parabola y=ax2 are A and B respectively. Connect OA and OB to find the area of ​​△AOB

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

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Update Time: 2024-11-21

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