"The relationship between quadratic functions and quadratic equations" PPT

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"The relationship between quadratic functions and quadratic equations" PPT

Part One: Review Questions

1. The discriminant of the roots of the quadratic equation ax2+bx+c=0(a≠0) is △ = ________.

The situation of the roots of the equation is: when △�0 the equation ______________;

When △=0, the equation ______________;

When △�0, the equation ________.

2. The image of the quadratic function y=ax2+bx+c (a, b, c are constants, and a≠0) is a ___________,

PPT on the relationship between quadratic functions and quadratic equations, part 2: independent learning

Independent learning one:

1. How many situations exist for the number of intersection points between the quadratic function image and the x-axis? Think about it, draw it

Three possibilities:

①Two intersection points

②An intersection point

③There is no intersection.

think about it

What is the relationship between the graph of the quadratic function y=ax2+bx+c and the coordinates of the x-axis intersection and the root of the quadratic power ax2+bx+c=0?

The abscissa of the intersection point with the x-axis is the value of the independent variable x when y=0

That is the root of the equation ax2+bx+c=0.

Independent study 2: What is the relationship between the graph of the quadratic function and the coordinates of the x-axis intersection and the roots of the quadratic equation?

Tracking exercise one

1. If the roots of the equation ax2+bx+c=0 are x1=-2 and x2=3, then the coordinates of the intersection of the graph of the quadratic function y=ax2+bx+c and the x-axis are ________.

2. The parabola y=x2-4x+4 has intersection points with the axis, and the coordinates are ________.

3. The intersection of parabola y=0.5x2-x+3 and the x-axis is ( )

A Two intersection points B One intersection C No intersection D Can only be explained after drawing a picture

4 Without drawing a graph, find the coordinates of the intersection of the parabola y=x2-3x-4 and the x-axis.

Solution: ∵ Solve the equation x2-3x-4=0 and get: x1=-1, x2=4

∴The intersection coordinates of the parabola y=x2-3x-4 and the x-axis are: (-1, 0) and (4, 0)

PPT on the relationship between quadratic functions and quadratic equations of one variable, part three: class summary

1. Determination of the number of intersections between the quadratic function y=ax2+bx+c and the X-axis

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

3. Use the intersection expression to find the expression of the quadratic function

Keywords: Free download of Hebei Education Edition mathematics PPT courseware for the second volume of ninth grade, PPT download on the relationship between quadratic functions and quadratic equations, .PPT format;

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"Relationship between Quadratic Functions and Quadratic Equations" PPT download:

"The Relationship between Quadratic Functions and Quadratic Equations" PPT Download Part One Content: Situation Introduction We already know that the relationship between the height h (m) of a vertically thrown object and the motion time t (s) can be expressed by the formula h=-5t2 +v0t+h0 means, where h0(m) is the height when thrown..

"The relationship between quadratic functions and quadratic equations" PPT courseware:

"The Relationship between Quadratic Functions and Quadratic Equations" PPT Courseware Part One Content: Classroom Problem When a ball is hit at an angle of 30 degrees to the ground at a speed of 40m/s, the flight path of the ball will be a parabola. If air resistance is not considered, the flying height of the ball is h(..

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Update Time: 2024-11-12

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

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