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第四章:部分分式 Partial Fraction

第六章:角的形成及单位 Angles and Measurements

第十三章: 方程组 Simultaneous Equations

第十五章:二元一次不等式及线性规划 linear inequality in two variables and linear programming

2.4 一元二次函数的图像及性质 Graph and Nature of Quadratic Equation
2.4 Graph and Nature of Quadratic Equation 一元二次函数的图像及性质


 
Sketch the following functions, state also their symmetric axis, extreme point, domain and range.
画出下列函数的图像,并写出它们的对称轴,顶点,定义域和值域。
 

[1] y = 2(x - 1)^2 + 1

 

Answer :
x = 1, (1, 1), D = R, R = [1, \infty)

[2] y = (4 - x)(2x + 1)

 

Answer :
x = 1\frac{2}{3}, (1\frac{2}{3}, 101\frac{1}{9}), D = R, R = (-\infty, 10\frac{1}{9}]
[3] y = 2x^2 +5x - 3
Answer :
x = -1\frac{1}{4}, (-1\frac{1}{4} , -6\frac{1}{8}), D = R, R = [-6\frac{1}{8}, \infty)
[4] y = 2x^2 - 3x + 2
Answer :
x = \frac{3}{4} , (\frac{3}{4}, \frac{7}{8}), D = R, R = [\frac{7}{8}, \infty)
[5] y = 1 - 3x - x^2
Answer :
x = -1\frac{1}{2}, (-1\frac{1}{2} , 3\frac{1}{4}), D = R, R = (-\infty, 3\frac{1}{4}]