"Graphics of quadratic functions and quadratic equations of one variable" PPT courseware 2

Description

"Graphics of quadratic functions and quadratic equations of one variable" PPT courseware 2

learning target

1. Experience the process of exploring the relationship between quadratic functions and quadratic equations, and understand the connection between equations and functions;

2. Use the graphical method to find the approximate roots of a quadratic equation of one variable.

New course introduction

Question: 1. The intersection coordinate of the linear function y=2x-4 and the x-axis is (,)

2. Tell me, how did you get it?

Let y=0 be substituted into the analytical expression of the function

Knowledge explanation

Question: As shown in the figure, when the ball is hit at an angle of 30° to the ground at a speed of 40m/s, the flight path of the ball will be a parabola. If the resistance of the air is not considered, the flying height of the ball h (unit : m) and the flight time t (unit: s) have a relationship: h=20t-5t2. Consider the following questions:

(1) Can the flying height of the ball reach 15m? If so, how much flight time is required?

(1) Solve equation 15=20t-5t2,

t2-4t+3=0，

t1=1,t2=3.

When the ball flies for 1s or 3s, its height is 15m.

(2) Can the flying height of the ball reach 20m? If so, how much flight time is required?

(3) Can the flying height of the ball reach 20.5m? If so, how much flight time is required?

(4) How long does it take for the ball to fly out and land on the ground?

As can be seen from the above, the quadratic function is closely related to the quadratic equation. For example, it is known that the value of the quadratic function y=-x2+4x is 3, and finding the value of the independent variable x can be regarded as solving the quadratic equation. -x2+4x=3 (i.e. x2 -4x+3=0).

In turn, solve the equation x2-4x+3=0,

It can also be regarded as knowing that the value of the quadratic function y=x2-4x+3 is 0, and the value of the independent variable x is found.

The two roots of the quadratic equation ax2+bx+c=0 are x1, x2, then the coordinates of the intersection of the parabola y=ax2+bx+c and the x-axis are (x1, 0), (x2, 0).

The intersection of the graph of the quadratic function y=ax2+bx+c and the x-axis

There are three situations:

(1) There are two intersection points b2–4ac > 0

(2) There is an intersection point b2–4ac= 0

(3) There is no intersection point b2–4ac< 0

If the parabola y=ax2+bx+c intersects with the x-axis, then b2 – 4ac≥0

Track training

1. The number of intersections between the quadratic function y=x2-2x+1 and the x-axis is ( )

A.0 B.1 C.2 D.3

2. If the parabola y=ax2+bx+c, when a>0, c<0, the intersection point of the image and the x-axis is ()

A. No intersection point B. Only one intersection point

C.There are two intersection points D.Cannot be determined

3. If the quadratic equation x2-2x+m=0 about x has two equal real roots, then m=＿＿. At this time, the parabola y=x2-2x+m has ＿＿intersection points with the x-axis.

4. The graph of the quadratic function y=ax2+bx+c(a≠0) is as shown in the figure, then which of the following statements is incorrect ()

A.b2-4ac>0 B.a>0

C.c>0 D.-b/2a<0

Summary of this lesson

Through the study of this class, we need to master:

1. From the quadratic equation ax2+bx+c=0 roots, the number of intersection points of the quadratic function y=ax2+bx+c and the x-axis can be determined;

2. Use the graphical method to find the approximate roots of a quadratic equation of one variable.

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

"Graphics of Quadratic Functions and Quadratic Equations of One Variable" PPT courseware:

"Graphics of Quadratic Functions and Quadratic Equations" PPT courseware learning objectives 1. Explore the relationship between the abscissa of the intersection of the parabola and the x-axis and the roots of the quadratic equation, and understand the close relationship between equations and functions; 2. Learn to use images Method to find the approximate roots of a quadratic equation; observe..

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Update Time: 2024-09-08

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

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