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

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

Exploration 1: What is the relationship between the quadratic function y=ax2+bx+c and the quadratic equation ax2+bx+c=0?

1. What is the relationship between the linear function y=kx+b and the linear equation kx+b=0?

2. Can you use analogy to guess the relationship between the quadratic function y=ax2+bx+c and the quadratic equation ax2+bx+c=0?

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 t 2

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?

induction

The abscissa of the intersection of the parabola y=ax2+bx+c and the x-axis is the root of the equation ax2+bx+c =0.

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)

Trial test

1. The two roots of the quadratic equation 3 x2+x-10=0 are x1= -2, x2=5/3, then the coordinates of the intersection of the quadratic function y= 3 x2+x-10 and the x-axis are ＿＿＿＿ .

2. Does the parabola y=2x2-3x-5 intersect with the x-axis? If there is no reason given, if so, can the coordinates of the intersection be found?

Practice in class

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

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 =＿＿.

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Update Time: 2024-10-20

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

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