"Quadratic Functions and Quadratic Equations of One Variable" Quadratic Function PPT Courseware 2

Description

"Quadratic Functions and Quadratic Equations of One Variable" Quadratic Function PPT Courseware 2

teaching objectives

knowledge and abilities

Summarize the relationship between the number of intersections of a quadratic function and the x-axis and the number of roots of a quadratic equation, and express when the equation has two unequal real roots, two equal real numbers, and no real roots.

Can use the graph of a quadratic function to find approximate solutions to quadratic equations of one variable.

Process and Method

Experience the process of exploring the relationship between quadratic functions and quadratic equations of one variable, and experience the connection between equations and functions.

Emotional attitudes and values

By observing the number of intersections between the graph of the quadratic function and the x-axis, we discuss the roots of the quadratic equation of one variable and further understand the idea of ​​combining numbers and shapes.

Important and difficult points in teaching

The relationship between quadratic functions and quadratic equations of one variable.

Use the graph of a quadratic function to find the real roots of a quadratic equation of one variable.

The relationship between the roots of quadratic equations and the relationship between the quadratic function image and the x-axis position, and the application of the idea of ​​combining numbers and shapes.

Use the graph of a quadratic function to find an approximate solution to a quadratic equation of one variable.

Explore

Does the graph of the following quadratic function intersect with the x-axis? If so, find the coordinates of the intersection.

(1) y = 2x2+x-3

(2) y = 4x2 - 4x +1

(3) y = x2 – x+ 1

The relationship between the graph of the quadratic function y=ax2+bx+c and the three cases of intersection of the x-axis and the roots of the quadratic equation of one variable

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

There are two intersection points

There is an intersection

No intersection

Root of ax2+bx+c = 0

b2 – 4ac > 0

b2 – 4ac = 0

b2 – 4ac < 0

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

1. The parabola that does not intersect the x-axis is ( )

A. y = 2x2 – 3 B. y=-2 x2 + 3

C. y= -x2 – 3x D. y= -2(x+1)2 -3

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

A. No intersection B. Only one intersection

C. There are two intersection points D. Unable to determine

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Update Time: 2024-11-22

This template belongs to Mathematics courseware People's Education Press Ninth Grade Mathematics Volume 1 industry PPT template

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