"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;

Keywords: Quadratic function courseware, Quadratic function graph and properties courseware, New People's Education Edition ninth grade mathematics PPT courseware, Ninth grade mathematics slide courseware download, Quadratic function PPT courseware download, Quadratic function graph and properties PPT courseware download, .ppt format

For more information about the "Quadratic Function Graphics and Properties of Quadratic Functions" PPT courseware, please click the Quadratic Function ppt Graphics and Properties of Quadratic Functions ppt tag.

"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..

File Info

Update Time: 2024-11-22

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

Preview