"Quadratic Functions and Quadratic Equations of One Variable" Quadratic Function PPT Courseware 6

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"Quadratic Functions and Quadratic Equations of One Variable" Quadratic Function PPT Courseware 6

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1. The axis of symmetry of the parabola y=x²+2x-4 is ______, the opening direction is _____, and the coordinates of the vertex are ________.

2. It is known that the parabola intersects with the x-axis at A(-1,0) and B(1,0), and passes through point M(0,1), then the analytical formula of this parabola is __________.

3. The intersection point of the parabola y=2(x-2)(x-3) with the x-axis is ___________, the intersection point with the y-axis is ______, and the root of the equation 2(x-2)(x-3)=0 for____.

4. The intersection point of parabola y=-5x²+40x and y=60 is ________, and the root of the equation -5x²+40x=60 is ________.

Do it, discuss it

Complete the following items and answer the questions:

1. Make the graph of the function y=x²+2x, and calculate the value of x when y=0.

Intersection points with the x-axis (-2, 0) and (0, 0)

Find the roots of the equation x²+2x=0.

Solution: From x(x+2)=0

Then the roots of this equation are: x1=-2, x2=0

2. Make the graph of the function y=x²-2x+1, and calculate the value of x when y=0.

Find the roots of the equation x²-2x+1=0.

Solution: From (x-1)²=0

Then the roots of this equation are: x1=x2=1

question:

1. What are the number of intersections between the quadratic function image and the x-axis?

Analysis: There are three situations where the graph of the quadratic function y=ax²+bx+c intersects with the x-axis:

1. There are two intersection points,

2. There is an intersection,

3. There is no intersection.

2. What is the relationship between the image of the quadratic function y=ax²+bx+c(a≠0) and the abscissa of the intersection point of the x-axis and the roots of the quadratic equation ax²+bx+c=0(a≠0)?

When the graph of the quadratic function y=ax²+bx+c (a≠0) intersects with the x-axis, the abscissa of the intersection is the value of the independent variable x when y=0, that is, the quadratic equation ax²+bx The root of +c=0(a≠0).

When is the quadratic function y=ax²+bx+c a quadratic equation? What is their relationship?

Generally speaking, when y takes a constant value, the quadratic function is a quadratic equation, and the value of x that makes y take a constant value is the root of the quadratic equation.

Thinking: What is the relationship between the roots of the equation -x²+2x+1=0 and the graph of the quadratic function y=-x²+2x+1?

Application examples

[Example] The relationship between the height h(m) of a vertically thrown object and its movement time t(s) can be expressed by the formula h=-5t²+v0t+h0, where h0(m) is the height when it is thrown, v0(m /s) is the speed when thrown. A small ball is thrown vertically upward from the ground at a speed of 40m/s. The relationship between the height h (m) of the small ball and the movement time t (s) is as shown in the figure, then :

(1) What is the relationship between h and t?

Solution: It is a quadratic function h=-5t²+40t.

(2) What do the horizontal and vertical coordinates of each point on the image mean?

Solution: The abscissa of each point on the image represents the movement time of the ball t (s), and the ordinate represents the height of the ball from the ground h (m).

(3) How many seconds does it take for the ball to hit the ground? How many ways do you have to solve it? Communicate with your peers.

Solution: The height of the ball from the ground when it hits the ground is h=0.

That is -5t²+40t=0, the solution is t=0s (rounded) t=8s. You can use the image.

Lesson Summary

Based on the content of this lesson, ask students to discuss and summarize: What is the relationship between quadratic functions and quadratic equations of one variable?

For the quadratic function y=ax²+bx+c, when y takes a constant value, the quadratic function is a quadratic equation, and the value of x that makes y take a constant value is the root of the quadratic equation.

Keywords: quadratic function, quadratic function and quadratic equation teaching courseware, Beijing Normal University edition ninth grade mathematics volume 2 PPT courseware, ninth grade mathematics slide courseware download, quadratic function, quadratic function and quadratic equation PPT courseware download, .ppt format

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Update Time: 2024-10-03

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