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【作品展示】

 

【作品介绍】

史上最全求解二次函数

部分功能待完善

求大佬指点

 

【作品源代码】

import matplotlib.pyplot as plt          # 导入matplotlib用于绘图
import numpy as np                       # numpy库用于科学计算
from fractions import Fraction as fa     # 用于显示分数

# 求解type1
def solve_type1():
    # 全局变量a, b, c, 作用类似于return
    global a, b, c
    # 若输入存在错误，不用手动重开程序，自动循环再次获取输入
    while True:
        x_collect = []      # 存放搜集到的点的x坐标数据
        y_collect = []      # 存放搜集到的点的y坐标数据
        num = input("请输入a, b, c中已知数量（0，1，2）:")
        if num == '0':
            '''
            for i in range(1, 4):
                x_collect.append(
                    fa(float(input("请输入第{}个点坐标的横坐标(x)：".format(i)))))
                y_collect.append(
                    fa(float(input("请输入第{}个点坐标的纵坐标(y)：".format(i)))))
            # y_collect[0]=a(x_collect[0]^2)+bx_collect[0]+c
            # y_collect[1]=a(x_collect[1]^2)+bx_collect[1]+c
            # y_collect[2]=a(x_collect[2]^2)+bx_collect[2]+c
            '''
            print('当前版本尚不支持，等待后续优化')
            break
        elif num == '1':
            collect_1 = input('''请输入已知量:
            e.g.:a 1 (两个量中使用空格隔开)：''').split(" ")
            # 输入错误处理
            if collect_1[0] != 'a' and 'b' and 'c':
                print("请输入符合规则的字符")
                continue
            # 数据采集
            for i in range(1, 3):
                x_collect.append(
                    fa(float(input("请输入第{}个点坐标的横坐标(x)：".format(i)))))
                y_collect.append(
                    fa(float(input("请输入第{}个点坐标的纵坐标(y)：".format(i)))))
            # 已知量为a
            if collect_1[0] == 'a':
                a = fa(float(collect_1[1]))
                b = fa(float(y_collect[1] - y_collect[0] -
                    a*(x_collect[1]+x_collect[0])))
                c = fa(float(y_collect[0] - a *
                    (x_collect[0]**2) - b*x_collect[0]))
                break
            # 已知量为b
            elif collect_1[0] == 'b':
                b = fa(float(collect_1[1]))
                a = fa(float((y_collect[1]-y_collect[0]-b) /
                    (x_collect[1]+x_collect[0])))
                c = fa(float(y_collect[0] - a *
                    (x_collect[0]**2) - b*x_collect[0]))
                break
            # 已知量为c
            elif collect_1[0] == 'c':
                c = fa(float(collect_1[1]))
                a_temp = (x_collect[1]*(y_collect[0]-c)-x_collect[0]*(y_collect[1]-c))/(x_collect[1]*(x_collect[0]**2)-x_collect[0]*(x_collect[1]**2))
                a = fa(float(a_temp))
                b_temp = ((y_collect[1]-c)*(x_collect[0]**2)-(y_collect[0]-c)*(x_collect[1]**2))/(x_collect[1]*(x_collect[0]**2)-x_collect[0]*(x_collect[1]**2))
                b = fa(float(b_temp))
                break
            # 输入错误处理
            else:
                print("请输入符合规则的字符")
        elif num == '2':
            for i in range(2):
                collect_1 = input('''请输入已知量:
                e.g.:a 1 (两个量中使用空格隔开)：''').split(" ")
                # 输入错误处理
                if collect_1[i] != 'a' and 'b' and 'c':
                    print("请输入符合规则的字符")
                    continue
            x_collect.append(
                    fa(float(input("请输入已知点坐标的横坐标(x)："))))
            y_collect.append(
                    fa(float(input("请输入已知点坐标的纵坐标(y)："))))
            if collect_1[0] == 'a' and collect_1[2] == 'b':
                a = collect_1[1]
                b = collect_1[3]
                c = y_collect[0] - a*(x_collect[0]**2) - b*x_collect[0]
            elif collect_1[0] == 'a' and collect_1[2] == 'c':
                a = collect_1[1]
                c = collect_1[3]
                b = (y_collect[0]-a*(x_collect[0]**2)-c) / x_collect[0]
            elif collect_1[0] == 'b' and collect_1[2] == 'c':
                b = collect_1[1]
                c = collect_1[3]
                a = (y_collect[0]-b*x_collect[0]-c) / x_collect[0]**2
            break
        # 输入错误处理
        else:
            print("请输入符合规则的字符")
            continue

# 求解type2
def solve_type2():
    global a, k, h
    while True:
        k = fa(float(input("请输入顶点坐标的横坐标x（e.g.:1）：")))
        h = fa(float(input("请输入顶点坐标的纵坐标y（e.g.:1）：")))
        x = fa(float(input("请输入已知点坐标的横坐标x：")))
        y = fa(float(input("请输入已知点坐标的纵坐标y：")))
        # 输入错误处理
        if y-h == 0 or x-k == 0:
            print("请输入除顶点外的点")
        else:
            a = (y-h) / ((x-k)**2)
            break

# 求解type3
def solve_type3():
    global a, x1, x2
    x1 = fa(float(input("请输入第一个交点的x坐标：")))
    x2 = fa(float(input("请输入第二个交点的x坐标：")))
    x = fa(float(input("请输入已知点坐标的横坐标x：")))
    y = fa(float(input("请输入已知点坐标的纵坐标y：")))
    a = fa(float((y)/((x-x1)*(x-x2))))


# 化简type1的解析式
def huajian_type1():
    global fun
    # 若a为0
    if a == 0:
        if b == 0:
            if c == 0:
                print("该函数不存在，请检查后重试")
                fun = None
            else:
                fun = f"y={c}"
        else:
            if c > 0:
                fun = f"y={b}x+{c}"
            elif c < 0:
                fun = f"y={b}x{c}"
    # 若a为1
    elif a == 1:
        if b == 0:
            if c == 0:
                fun = f"y=x^2"
            elif c > 0:
                fun = f"y=x^2+{c}"
            elif c < 0:
                fun = f"y=x^2{c}"
        elif b > 0:
            if c == 0:
                fun = f"y=x^2+{b}x"
            elif c > 0:
                fun = f"y=x^2+{b}x+{c}"
            elif c < 0:
                fun = f"y=x^2+{b}x{c}"
        elif b < 0:
            if c == 0:
                fun = f"y=x^2{b}x"
            elif c > 0:
                fun = f"y=x^2{b}x+{c}"
            elif c < 0:
                fun = f"y=x^2{b}x{c}"
    # 其他情况
    else:
        if b == 0:
            if c == 0:
                fun = f"y={a}x^2"
            elif c > 0:
                fun = f"y={a}x^2+{c}"
            elif c < 0:
                fun = f"y={a}x^2{c}"
        elif b > 0:
            if c == 0:
                fun = f"y={a}x^2+{b}x"
            elif c > 0:
                fun = f"y={a}x^2+{b}x+{c}"
            elif c < 0:
                fun = f"y={a}x^2+{b}x{c}"
        elif b < 0:
            if c == 0:
                fun = f"y={a}x^2{b}x"
            elif c > 0:
                fun = f"y={a}x^2{b}x+{c}"
            elif c < 0:
                fun = f"y={a}x^2{b}x{c}"
    if fun != None:
        print("解析式为:"+fun)

# 化简type2
def huajian_type2():
    global fun
    if a == 0:
        if h == 0:
            print("该函数不存在，请检查后重试")
            fun = None
        else:
            fun = f'y={h}'
    elif a == 1:
        if h == 0:
            if k == 0:
                fun = f'x^2'
            elif k > 0:
                fun = f'y=(x-{k})^2'
            elif k < 0:
                fun = f'y=(x+{-k})^2'
        elif h > 0:
            if k == 0:
                fun = f'y=x^2+{h}'
            elif k > 0:
                fun = f'y=(x-{k})^2+{h}'
            elif k < 0:
                fun = f'y=(x+{-k})^2+{h}'
        elif h < 0:
            if k == 0:
                fun = f'y=x^2{h}'
            elif k > 0:
                fun = f'y=(x-{k})^2{h}'
            elif k < 0:
                fun = f'y=(x+{-k})^2{h}'
    else:
        if h == 0:
            if k == 0:
                fun = f'y={a}x^2'
            elif k > 0:
                fun = f'y={a}(x-{k})^2'
            elif k < 0:
                fun = f'y={a}(x+{-k})^2'
        elif h > 0:
            if k == 0:
                fun = f'y={a}x^2+{h}'
            elif k > 0:
                fun = f'y={a}(x-{k})^2+{h}'
            elif k < 0:
                fun = f'y={a}(x+{-k})^2+{h}'
        elif h < 0:
            if k == 0:
                fun = f'y={a}x^2{h}'
            elif k > 0:
                fun = f'y={a}(x-{k})^2{h}'
            elif k < 0:
                fun = f'y={a}(x+{-k})^2{h}'
    if fun != None:
        print("解析式为:"+fun)

# 化简type3
def huajian_type3():
    global fun
    if a == 0:
        print("该函数不存在，请检查后重试")
        fun = None
    elif a == 1:
        if x1 == 0:
            if x2 == 0:
                fun = f'y=x^2'
            elif x2 > 0:
                fun = f'y=x(x-{x2})'
            elif x2 < 0:
                fun = f'y=x(x+{-x2})'
        elif x1 > 0:
            if x2 == 0:
                fun = f'y=x(x-{x1})'
            elif x2 > 0:
                fun = f'y=(x-{x1})(x-{x2})'
            elif x2 < 0:
                fun = f'y=(x-{x1})(x+{-x2})'
        elif x1 < 0:
            if x2 == 0:
                fun = f'y=x(x+{-x1})'
            elif x2 > 0:
                fun = f'y=(x+{-x1})(x-{x2})'
            elif x2 < 0:
                fun = f'y=(x+{-x1})(x+{-x2})'
    else:
        if x1 == 0:
            if x2 == 0:
                fun = f'y={a}(x^2)'
            elif x2 > 0:
                fun = f'y={a}x(x-{x2})'
            elif x2 < 0:
                fun = f'y={a}x(x+{-x2})'
        elif x1 > 0:
            if x2 == 0:
                fun = f'y={a}x(x-{x1})'
            elif x2 > 0:
                fun = f'y={a}(x-{x1})(x-{x2})'
            elif x2 < 0:
                fun = f'y={a}(x-{x1})(x+{-x2})'
        elif x1 < 0:
            if x2 == 0:
                fun = f'y={a}x(x+{-x1})'
            elif x2 > 0:
                fun = f'y={a}(x+{-x1})(x-{x2})'
            elif x2 < 0:
                fun = f'y={a}(x+{-x1})(x+{-x2})'
    if fun != None:
        print("解析式为:"+fun)

# 绘制函数图像
def create_graph(a, b, c, d=-10, e=10):  # d,e分别是x的取值范围
    x = np.arange(d, e, 0.01)
    y = a*(x**2)+b*x+c
    plt.plot(x, y)
    plt.rcParams['font.sans-serif']=['SimHei']  #用来正常显示中文标签
    plt.rcParams['axes.unicode_minus']=False    #用来正常显示负号
    plt.title("解析式为"+fun+"的图像")
    # plt.legend('best')
    point_x = b / -2*a
    point_y = a*(point_x**2)+b*point_x+c
    plt.scatter(point_x, point_y, c='r')
    plt.text(point_x + 0.5,point_y - 5,f"顶点坐标({point_x},{point_y})",
             fontsize=12,color='r')
    plt.show()

# 类型采集
Input = input('''请输入二次函数类型：
        \t type1（一般式）:y=ax^2+bx+c      （请输入1）
        \t type2（顶点式）:y=a(x-k)^2+h     （请输入2）
        \t type3（交点式）:y=a(x-x1)(x-x2)  （请输入3）:''')

while True:
    if Input == '1':
        solve_type1()
        huajian_type1()
        if fun != None:
            create_graph(a, b, c)
            break
    elif Input == '2':
        solve_type2()
        huajian_type2()
        # 化简得y=ax^2-2akx+k^2+h
        if fun != None:
            create_graph(a, -2*a*k, k**2+h)
            break
    elif Input == '3':
        solve_type3()
        huajian_type3()
        # 化简得y=ax^2-a(x2+x1)x+ax1x2
        if fun != None:
            create_graph(a, -a*(x2+x1), a*x1*x2)
            break
    else:
        print("请输入符合规则的字符")

 

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