"Quadratic Functions and Quadratic Equations of One Variable" Quadratic Function PPT Courseware 7

Description

"Quadratic Functions and Quadratic Equations of One Variable" Quadratic Function PPT Courseware 7

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.

Practical problems

When a ball is hit at a speed of 40 m/s in a direction that is 30° to the ground, the flight path of the ball is a parabola. If air resistance is not considered, the flight height h (unit: m) of the ball is equal to the flight time There is a relationship between t (unit: s): h= 20 t – 5 t²

Consider the following questions:

(1) Can the flying height of the ball reach 15 m? If so, how long does it take?

(2) Can the flying height of the ball reach 20 m? If so, how long does it take?

(3) Can the flying height of the ball reach 20.5 m? Why?

(4) How long does it take for the ball to fly from flying out to landing?

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

Practice in class

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

A. y = 2x² – 3 B. y=-2x²+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

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. It is known that the vertex of the parabola y=x² – 8x + c is on the x-axis, then c =＿＿.

5. If the vertex of the parabola y=x²+ bx+ c is in the first quadrant, then the root of the equation x²+bx+c=0 is ＿＿＿＿＿.

summary

Repeating the above steps, we gradually get: this root is between 2.625, 2.75, between 2.6875, 2.75... we can get:

The range where the root is located is getting smaller and smaller, and the values ​​at both ends of the range where the root is located are getting closer and closer to the value of the root, so it can be used as an approximate value of the root. For example, when the absolute value of the difference between the approximate value of the root and the exact value of the root is required to be less than When 0.1, since |2.6875-2.75|=0.0625<0.1, we can use 2.6875 as the approximate value of the root.

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Update Time: 2024-09-25

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