"Quadratic Functions and Quadratic Equations of One Variable" Quadratic Function PPT Courseware 3

Description

"Quadratic Functions and Quadratic Equations of One Variable" Quadratic Function PPT Courseware 3

teaching objectives:

1. Understand the relationship between the intersection point of the parabola y=ax²+bx+c and the x-axis and the root of the equation ax²+bx+c=0.

2. Understand the correspondence between the positional relationship between the graph of the quadratic function y=ax²+bx+c and the x-axis and the root of the quadratic equation ax²+bx+c=0.

3. Master the method of combining numbers and shapes to solve problems.

reading textbook

Thinking: 1. What is the basis for whether the required height can be achieved?

2. Why does the ball have two flight times when its height is 15 meters and 0 meters? And there is only one time to reach 20 meters?

Knowledge inquiry

Question 1: As shown in the figure, when a ball is hit at a speed of 40 m/s in a direction of 30 degrees with the ground, the flight path of the ball is a parabola. If air resistance is not considered, the flight height of the ball is y (unit :m) and flight time x (unit: s) have a relationship: y= 20 x – 5 x²

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? If so, how long will it take?

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

induction:

The relationship between y=ax²+bx+c and ax²+bx+c=0:

1. Solving the equation ax²+bx+c=0 can be regarded as finding the value of the independent variable x when the value of the quadratic function y=ax²+bx+c is 0.

Find the value of the independent variable x when the value of the quadratic function y=ax²+bx+c is 0. It can be seen as solving the equation ax²+bx+c=0

Question 2: Does the graph of the following quadratic function have an intersection with the x-axis? If so, please find the coordinates of the intersection.

(1) y = x²+x-2

(2) y = x² - 6x +9

(3) y = x² – x+ 1

In-class training

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

2. 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

3. The graph of the quadratic function is shown in Figure 6. Which of the following relational expressions is incorrect ( )

A.a<0 B.abc>0

C.a+b+c>0 D.b²-4ac>0

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

Knowledge improvement:

1. 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 ＿＿＿＿＿.

2. The straight line y=2x+1 and the parabola y= x²+4x+3 have __________ intersection points.

3. Known parabola y=x²+mx+m-2

Prove: No matter what value m takes, the parabola always has two intersection points with the x-axis.

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Update Time: 2024-07-06

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