二次函数导学案

二次函数导学案

Chapter 22 Quadratic ns

22.1 Graphs and Properties of Quadratic ns

22.1.1 Quadratic ns

Activity 1: Knowledge n

1.y = 3x - 1 is a n。y = x is both a linear n and a n.

2.For the n y = (m+1)x^2.when m=0.the n is a XXX.

Activity 2: Textbook Guidance

Concept of Quadratic ns

1) If the side length of a square is x cm and its area is y

cm^2.then the n nship een y and x is ___。Since x^2 is a quadratic term。it (is/is not) a linear n.

2) If an 800 cm long wooden strip is used to make a rectangular window frame。and one side has a length of x cm。then the n nship een the area y cm^2 and x cm is ___。To make the independent variable x meaningful。its range of values is ___.

3) What is the common feature of the above two ns?

Knowledge Point 1: n of Quadratic ns

Generally。a n in the form of (a。b。c are constants,) is called a quadratic n。Here。x is the independent variable。and a。b。and c are the coefficients of the n.

Knowledge Point 2: XXX

In general。the range of values for the independent variable

of a quadratic n is ___。In practical problems。the values of the independent variable must be meaningful.

Exploring Problem 1: n of Quadratic ns

Example 1: Which of the following XXX x?

1) y = 9x^2 - x。(2) y = -x^2.(3) y = 4 - x + x^3.(4) y = 2x^3;

5) y = (x-1)^2 - (x+1)(x-2)。(6) y = ax^2 + 4x + 1.

Summary] To determine whether a n is a quadratic n。it must first be XXX n containing the independent variable satisfies the XXX: (1) it is a quadratic n of the independent variable。(2) it does not contain any higher-order terms of the independent variable。(3) the coefficient of the quadratic term is not zero.

Exploring Problem 2: XXX

Example 2: [Textbook Problem 1 n Problem] During the summer n。the n students in Class 9(8) agreed to make a phone call to each other once.

1) Write the n n for the number of phone calls m een two students as a n of n。and indicate what n of n m is;

2) When n = 10.how many phone calls are made?

1.Multiple Choice ns

1.Which of the following XXX。(A) y = x(x+1) (B) xy = 1

(C) y = 2x^2 - 2(x+1)^2 (D) y = 3x^2 + 1

2.Which of the following practical problems XXX model?

① XXX een the maximum number of heartbeats per minute b

a person can XXX circumstances and the person's age a is

b =

0.8(220-a);

② XXX een the volume V of a cone with height h and the radius r of its base is V = πr^2h (h is constant);

③ XXX een the height h and the falling time t of an object in free fall is h = gt^2 (g is constant);

④ None of the above.

个图象叫做“抛物线”。

2）二次函数y＝ax2的图象