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【作品展示】

 

【作品介绍】

解一元二次方程 1.0.8

范围：实数内

编写兼构思：符海洲

（现上海市育民中学高一三班学生）

微信交流：lovediaoTang

创作日期：2023年03月05号

原创不易，转载请标明来源。

 

【作品源代码】

X = input("输入自变量=")
Y = input("输入因变量=")
a = eval(input("二次项系数（注意是否是二次函数）a="))
if a != 0:
    b = eval(input("一次项系数b="))
    c = eval(input("常数项c="))
    A = b*b-4*a*c
    print("---------------------------------------------------------------")
    if A == 0:
        X1 = (-b-(b*b-4*a*c)**(1/2))/(2*a)
        print("与", X, "轴有一个交点,坐标为(", X1, ",0)")
        X3 = -b/(2*a)
        X4 = (4*a*c-b*b)/(4*a)
        X5 = -b/a
        X6 = c/a
        print("---------------------------------------------------------------")
        print(X, "轴交点=", X1)
        print("---------------------")
        print("对称轴直线", X, "=", X3)
        if a < 0:
            print("最高点", Y, "取值=", X4)
        else:
            print("最低点", Y, "取值=", X4)
        print("---------------------")
        print("韦达定理", X, "₁+", X, "₂=", X5)
        print("韦达定理", X, "₁x", X, "₂=", X6)
        print("---------------------------------------------------------------")
        if X1 > 0:
            print("交点式", Y, "=", a, X, "(", X, "-", X1, ")")
        else:
            print("交点式", Y, "=", a, X, "(", X, X1, ")")
        print("---------------------------------------------------------------")
        if X3 > 0:
            print("顶点式", Y, "=", a, "(", X, "-", X3, ")²+", X4)
        else:
            print("顶点式", Y, "=", a, "(", X, X3, ")²+", X4)
        print("---------------------------------------------------------------")
        print("顶点(", X3, ",", X4, ")")
        if a > 0:
            print("开口向上")
        else:
            print("开口向下")
    elif A > 0:
        X1 = (-b-(b*b-4*a*c)**(1/2))/(2*a)
        X2 = (-b+(b*b-4*a*c)**(1/2))/(2*a)
        print("与", X, "轴有两个交点,坐标分别为(", X1, ",0),(", X2, ",0)")
        X3 = -b/(2*a)
        X4 = (4*a*c-b*b)/(4*a)
        X5 = -b/a
        X6 = c/a
        print("---------------------------------------------------------------")
        print(X, "轴左交点=", X1)
        print(X, "轴右交点=", X2)
        print("---------------------")
        print("对称轴直线", X, "=", X3)
        if a < 0:
            print("最高点", Y, "取值=", X4)
        else:
            print("最低点", Y, "取值=", X4)
        print("---------------------")
        print("韦达定理", X, "₁+", X, "₂=", X5)
        print("韦达定理", X, "₁x", X, "₂=", X6)
        print("---------------------------------------------------------------")
        if X1 > 0:
            if X2 > 0:
                print("交点式", Y, "=", a, "(", X, "-", X1, ")(", X, "-", X2, ")")
            else:
                print("交点式", Y, "=", a, "(", X, "-", X1, ")(", X, X2, ")")
        else:
            if X2 > 0:
                print("交点式", Y, "=", a, "(", X, X1, ")(", X, "-", X2, ")")
            else:
                print("交点式", Y, "=", a, "(", X, X1, ")(", X, X2, ")")
        print("---------------------------------------------------------------")
        if X3 > 0:
            print("顶点式", Y, "=", a, "(", X, "-", X3, ")²+", X4)
        else:
            print("顶点式", Y, "=", a, "(", X, X3, ")²+", X4)
        print("---------------------------------------------------------------")
        print("顶点(", X3, ",", X4, ")")
        if a > 0:
            print("开口向上")
        else:
            print("开口向下")
    else:
        print("与", X, "轴无交点")
        X3 = -b/(2*a)
        X4 = (4*a*c-b*b)/(4*a)
        print("---------------------------------------------------------------")
        print("对称轴直线", X, "=", X3)
        if a < 0:
            print("最高点", Y, "取值=", X4)
        else:
            print("最低点", Y, "取值=", X4)
        print("---------------------------------------------------------------")
        if X3 > 0:
            print("顶点式", Y, "=", a, "(", X, "-", X3, ")²+", X4)
        else:
            print("顶点式", Y, "=", a, "(", X, X3, ")²+", X4)
        print("---------------------------------------------------------------")
        print("顶点(", X3, ",", X4, ")")
        if a > 0:
            print("开口向上")
        else:
            print("开口向下")
elif a == 0:
    print("该函数不是二次函数")

 

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