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Authoritative PPT Summary
"Brake Distance and Quadratic Function" Quadratic Function PPT Courseware
learning target
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 influence of a and c on the graph of the quadratic function.
2. Process and methods
1. Through the process of exploring the methods and properties of the graphs of quadratic functions y=ax2 and y=ax2+c, you can further gain experience in connecting tables, expressions, and graphs.
2. By comparing the images and properties of y=ax2, y=ax2+c and y=x2, students can develop their comparison and identification abilities.
3. Emotions and values
1. From the relationship between "braking distance" and quadratic function. Understand that quadratic functions are mathematical models of some practical problems.
2. Through interesting practical problems, students can actively participate in mathematics learning activities and become curious and curious about mathematics.
Teaching focus
1. Be able to draw the images of y=ax2 and y=ax2+c, compare their similarities and differences with y=x2, and understand the influence of a and c on the image of quadratic functions.
2. Can tell the opening direction of the y=ax2 and y=ax2+c images; the symmetry axis and vertex coordinates.
Teaching difficulties
Can draw graphs of functions y=ax2 and y=ax2+c, summarize their properties, and compare with y=x2.
Preparation of teaching aids
Multimedia courseware, graph paper, simple drawing tools
Academic analysis
① Students have mastered how to draw the graph of the quadratic function y=x2 and the properties of their graphs.
②Students have acquired the ability to explore in group activities and have a good foundation for further research on quadratic functions y=ax2 and y=ax2+c
③The polarization of ninth-grade students is relatively serious, and it is particularly important to strengthen stratified teaching.
Discuss
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.
What is the shape of the graph of the quadratic function y=3x2-1? What are the similarities and differences between it and the graph of the quadratic function y=3x2? What are its opening direction, symmetry axis and vertex coordinates?
Think about it, what would it be like to draw the graphs of the quadratic functions y=-3x2-1 and y=-3x2 in the same coordinate system?
Example navigation
It is known that the straight line y=-2x+3 and the parabola y=ax2 intersect at two points A and B, and the coordinates of point A are (-3, m).
(1) Find the values of a and m;
(2) Find the expression of the parabola and its symmetry axis and vertex coordinates;
(3) When x takes on any value, y in the quadratic function y=ax2 decreases as x increases;
(4) Find the area of the triangle formed by two points A and B and the vertices of the quadratic function y=ax2.
Compliance in court
1. The opening of the parabola y=-4x2-4 is toward _____. When x=_____, y has the maximum _____ value, y=_____.
2. When m=_____, y=(m-1)xm²+m-3m is a quadratic function about x.
3． There are two points A (x, -27) and B (2, y) on the parabola y=-3x2, then x=_____, y=_____.
4. When m=_____, the parabola y=(m+1)xm²+m+9 opens downward, and the axis of symmetry 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 x and _____.
5. The intersection point of parabola y=3x2 and straight line y=kx+3 is (2, b), then k=_____, b=_____.
I gain, I make progress
1. Discuss in groups. What did you gain from this lesson?
2. After studying this lesson, what areas do you still need to work on further?
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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 2:
"Brake Distance and Quadratic Function" Quadratic Function PPT Courseware 2 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..