"Graphics and Properties of Quadratic Functions" Quadratic Function PPT Courseware 2

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"Graphics and Properties of Quadratic Functions" Quadratic Function PPT Courseware 2

Knowledge review

1. What are the characteristics of the graph of a linear function?

The graph of a linear function is a straight line.

When k>0, y increases with the increase of x;

When k<0, y decreases as x increases.

2. What are the characteristics of the image of the inverse proportional function?

The graph of an inverse proportional function is _______, has _______ branches, and is symmetric about _______.

When _______, the image is in the _______ quadrant, and y decreases as x increases in each quadrant;

When _______, the image is in the _______ quadrant, and y increases with x in each quadrant.

Thinking: What are the characteristics of this quadratic function graph?

(1) The shape is a parabola with an upward opening

(2) The image is symmetrical about the y-axis

(3) There is a lowest point but no highest point

The graph of the quadratic function y = x2 is a curve. Its shape is similar to the path the ball takes in the air when shooting, except that this curve opens upward. This curve is called a parabola y= x².

The graph of a quadratic function is a parabola.

Generally, the graph of the quadratic function y = ax² + bx + c (a≠0) is called a parabola y = ax² + bx + c

The y-axis is the axis of symmetry of the parabola y = x 2. The intersection point (0,0) of the parabola y = x 2 and its axis of symmetry is called the vertex of the parabola y = x2, which is the lowest point of the parabola y = x 2.

In fact, every parabola has an axis of symmetry, and the intersection of the parabola and the axis of symmetry is called the vertex of the parabola. The vertex is the lowest or highest point of the parabola.

practise

1. Translate the parabola y=1/2x² downward by 2 units to obtain the parabola __________, and then translate it upward by 5 units to obtain the parabola __________;

2. For the function y= –x2+1, when x__________, the function value y increases with the increase of x; when x__________, the function value y decreases with the increase of x; when x__________, The function that obtains the maximum __________ value is __________.

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"Graphics and Properties of Quadratic Functions" Quadratic Function PPT Courseware 3:

"Image and Properties of Quadratic Functions" Quadratic Function PPT Courseware 2 1. It is known that the parabola y=ax2+bx+c When x=1, y=0, then a+b+c=0 passes through the point (-10 ), then a-b+c=0 passes through point (0-3), then c=-3 passes through point (45), then 16a+4b+c=5 symmetry axis..

"Graphics and Properties of Quadratic Functions" Quadratic Function PPT courseware:

"Graphics and Properties of Quadratic Functions" Quadratic Function PPT Courseware Knowledge Review 1. What is the general form of a quadratic function? y=ax+bx+c (abc is the constant a 0) The graph of quadratic function y = x2 is a curve, its shape is similar to the path of the ball in the air when shooting...

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Update Time: 2024-10-05

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

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