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

Description

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

Knowledge review

1. What is the general form of a quadratic function?

y=ax²+bx+c(a, b, c are constants, a≠ 0)

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.

In fact, the graphs of quadratic functions are all parabolas. Generally, the graph of the quadratic function y = ax2 + bx + c (a≠0) is called a parabola y = ax2 + bx + c

The graph of the quadratic function y = x 2 is an axis-symmetric graph, and the axis of symmetry is the y-axis

2. When a>0, the parabola y=ax2 is above the x-axis (except for the vertex), its opening is upward, and it extends upward infinitely;

When a<0, the parabola y=ax2 is below the x-axis (except for the vertex), its opening is downward, and it extends downward infinitely.

3. When a>0, on the left side of the symmetry axis, y decreases as x increases; on the right side of the symmetry axis, y increases as x increases. When x=0, the function y has the smallest value.

When a<0, on the left side of the symmetry axis, y increases as x increases; on the right side of the symmetry axis, y decreases as x increases. When x=0, the function y The value is the largest.

Do it

(1) The vertex coordinate of the parabola y=2x2 is _______, and the axis of symmetry is _______. On the _______ side of the symmetry axis, y increases with the increase of x; on the _______ side of the symmetry axis, y increases with It decreases with the increase of x. When x=_______, the value of function y is minimum, and the minimum value is _______. The parabola y=2x2 is in the _______ square of the x-axis (except for the vertex).

(2) Parabola y=-2/3x² is on the _______ side of the x-axis (except the vertex). On the left side of the symmetry axis, y follows _______ of x; on the right side of the symmetry axis, y follows x Of _______, when x=0, the value of function y is the largest, and the maximum value is _______. When x_______0, y<0.

summary

1. What is the graph of the quadratic function y=ax2?

2. What are the properties of the graph of the quadratic function y=ax2?

3. What is the relationship between parabola y=ax2 and y=-ax2?

It is known that the graph of the quadratic function y=ax² passes through the point (-2, -3).

(1) Find the value of a and write the analytical formula of the function;

(2) State the vertex coordinates, symmetry axis, opening direction and position of the graph of the function;

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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 2:

"Graphics and Properties of Quadratic Functions" Quadratic Function PPT Courseware 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 k0, y increases as x increases; when k0, y decreases as x increases..

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Update Time: 2024-09-28

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

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