"Brake Distance and Quadratic Function" Quadratic Function PPT Courseware 2

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"Brake Distance and Quadratic Function" Quadratic Function PPT Courseware 2

think about it

Do you know why two cars must keep a certain distance when driving?

What factors determine the distance a car slides forward when braking (called braking distance)?

The most important factors affecting the braking distance are the speed of the car and the friction coefficient of the road surface. Studies have shown that when driving on a certain section of road on a sunny day, the braking distance s (m) of a car with a speed of v (km/h) can be calculated by Formula (1) determines:

When driving in rainy days, it is calculated by formula (2):

(1)s=1/100v² (2)s=1/50v²

Do it

The image and properties of function y=ax2(a≠0)

Draw the graphs of the quadratic functions y=x2 and y=2x2 in the same coordinate system.

(1) Complete the following table:

(2) Make the images of y=x2 and y=2x2 respectively.

(3) What is the shape of the graph of the quadratic function y=2x2? What are the similarities and differences between it and the graph of the quadratic function y=x2? What are its opening direction, symmetry axis and vertex coordinates?

The shape of the graph of the quadratic function y=2x2 is the same as y=x2, which is still a parabola.

Think about it, what would it be like to draw the images of quadratic functions y=-x2 and y=-2x2 in the same coordinate system?

Properties of the quadratic function y=ax2

1. The vertex of the parabola y=ax2 is the origin, and the axis of symmetry is the y-axis.

2. When a>0, the parabola y=ax2 is above the x-axis (except for the vertex), its opening is upward, and it extends upward infinitely; when a<0, the parabola y=ax2 is below the x-axis (except for the vertex) outside the apex), its opening is downward, and it extends downward infinitely.

3. When a>0, on the left side of the symmetry axis, y decreases as x increases; on the right side of the symmetry axis, y increases as x increases. When x=0, the function y has the smallest value. When a<0, on the left side of the symmetry axis, y increases as x increases; on the right side of the symmetry axis, y decreases as x increases, when x=0 , the value of function y is the largest.

4. The larger the |a|, the smaller the opening.

The smaller the |a|, the larger the opening.

I think, I progress

Draw the graph of the quadratic function y=2x²+1 and the graph of the quadratic function y=2x² in the same coordinate system.

What is the relationship between the graph of the quadratic function y=2x²+1 and the graph of the quadratic function y=2x²? Are they axially symmetrical graphs? What are its opening direction, axis of symmetry and vertex coordinates? Let’s take a look at the graph. look.

Summary and expansion

The relationship between the quadratic function y=ax²+c and =ax²

1. Similar points: (1) The images are all parabolas, with the same shape and the same opening direction.

(2) They are all axis-symmetric figures, and the axes of symmetry are all y-axis.

(3) There is a maximum (large or small) value.

(4) When a>0, the opening is upward. On the left side of the y-axis, y decreases with the increase of x. On the right side of the y-axis, y increases with the increase of x. When a<0, With the opening downward, on the left side of the y-axis, y increases as x increases, and on the right side of the y-axis, y decreases as x increases.

2. Different points: (1) Different vertices: (0,c), (0,0) respectively.

(2) The maximum values ​​are different: c and 0 respectively.

3. Connection: The image of y=ax²+c(a≠0) can be regarded as the image of y=ax² that is obtained by shifting the whole unit along the y-axis by c units. (When c>0 Translate upward; when c<0, translate downward).

exercise

1. What is the relationship between the graph of the quadratic function y=-3x² and y=3x²? Is it an axially symmetrical figure? What are its opening direction, axis of symmetry and vertex coordinates? Think about it first, and make a sketch if necessary. one look.

What about the quadratic functions y=-1/2x² and y=1/2x²?

2. What is the relationship between the graph of the quadratic function y=3x²+1/2 and y=3x²? Is it an axially symmetrical figure? What are its opening direction, axis of symmetry and vertex coordinates? Think about it first, if necessary, Take a look at the sketch.

What about the quadratic functions y=-1/2x²+3 and y=-1/2x²?

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"Brake Distance and Quadratic Function" Quadratic Function PPT Courseware 3:

"Brake Distance and Quadratic Function" Quadratic Function PPT Courseware 3 Think about it. Do you know why two cars keep a certain distance when driving? What factors are related to the distance a car slides forward when braking (called the braking distance) ? The most important factor affecting braking distance..

"Brake Distance and Quadratic Function" Quadratic Function PPT courseware:

"Brake Distance and Quadratic Function" Quadratic Function PPT Courseware Learning Objectives 1. Knowledge and Skills 1. The images of y=ax2 and y=ax2+c can be made. and study their properties. 2. Compare the similarities and differences between the images of y=ax2 and y=ax2+c and y=x2. Understand the pair a and c..

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Update Time: 2024-11-22

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