"Determining the Expression of a Quadratic Function" PPT courseware

Description

"Determining the Expression of a Quadratic Function" PPT courseware

learning target

1. Be able to use the undetermined coefficient method to find the expression of a quadratic function; (key point)

2. Able to set up the expression form of the corresponding quadratic function based on known conditions, and find the expression of the quadratic function more easily. (difficulty)

Review before class

What expressions are there for quadratic functions?

General formula: y=ax2+bx+c(a≠0)

Vertex formula: y=a(x-h)2+k(a≠0)

Intersection formula: y=a(x-x1)(x-x2)(a≠0)

Consolidation exercises

1. It is known that the symmetry axis of the quadratic function is x=2 and passes through two points (3, 2) and (-1, 10). Find the expression of the quadratic function.

Solution: Let y=a(x-2)2+k

2. It is known that the maximum value of the quadratic function is 2, and passing through the two points (3, 1) and (-1, 2), find the expression of the quadratic function.

Solution: Let y=a(x-h)2+2

Lectures on examples

Example 1: It is known that the vertex of the parabola is (-1, -6). Find the expression of the parabola passing through the point (2, 3)?

Note: Finally, the expression becomes a general form

Example 2: Given the points A (-1,6), B (4,6) and C (3,2), find the expression of the quadratic function passing through these three points.

a quadratic function,

When the independent variable x=1, the function value y=-2

When the independent variable x=-1, the function value y=-6. When the independent variable x=0, the function value y=-3. Find the analytical formula of this quadratic function?

Class summary

General method for finding the expression of a quadratic function:

The corresponding values ​​of three points or three pairs on the image are known, and the general formula is usually selected.

When the vertex coordinates of the image are known, the vertex formula is usually selected

It is known that the coordinates of the intersection point of the image and the x-axis are usually selected as the intersection formula

When determining the expression of a quadratic function, a function expression should be appropriately selected based on the characteristics of the conditions.

Find the analytical expression of the quadratic function of x according to the following conditions

1. When x=3, the minimum value of y=-1, and the image is over (0, 7)

2. The image passes through the points (0, -2) (1, 2) and the axis of symmetry is a straight line x=1.5

3. When x=1, y=0; when x=0, y=-2, when x=2, y=3;

4. The vertex coordinates are (-1, -2) and pass through the point (1, 10)

5. The axis of symmetry is x=2, the minimum value of the function is 3, and the image passes through the point (-1,5).

General steps for finding function expressions using the method of undetermined coefficients:

1. Set up a suitable function expression;

2. Substitute the known conditions into the function expression to obtain an equation or system of equations about the undetermined coefficients;

3. Solve the equation (set) to find the value of the undetermined coefficient;

4. Write the general formula.

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Update Time: 2024-09-05

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

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