# /// script
# requires-python = ">=3.11"
# dependencies = ["numpy", "matplotlib"]
# ///

import numpy as np
import matplotlib.pyplot as plt

# 设置中文字体
plt.rcParams['font.sans-serif'] = ['WenQuanYi Micro Hei', 'Noto Sans CJK SC', 'Microsoft YaHei', 'SimHei', 'SimSun', 'DejaVu Sans']
plt.rcParams['axes.unicode_minus'] = False

# 创建图形
fig, ax = plt.subplots(figsize=(10, 8), dpi=150)

# 定义函数 y = -2x² + 8x - 3
def f(x):
    return -2*x**2 + 8*x - 3

# 顶点坐标
x_vertex = 2
y_vertex = 5

# 生成 x 值范围（以顶点为中心，左右各延伸适当距离）
x = np.linspace(-1, 5, 500)
y = f(x)

# 绘制抛物线
ax.plot(x, y, 'b-', linewidth=2.5, label=r'$y = -2x^2 + 8x - 3$')

# 标注顶点
ax.plot(x_vertex, y_vertex, 'ro', markersize=12, zorder=5, label=f'顶点 ({x_vertex}, {y_vertex})')
ax.annotate(f'顶点\n({x_vertex}, {y_vertex})', 
            xy=(x_vertex, y_vertex), 
            xytext=(x_vertex + 0.8, y_vertex + 0.5),
            fontsize=12,
            ha='left',
            arrowprops=dict(arrowstyle='->', color='red', lw=1.5))

# 绘制对称轴
ax.axvline(x=x_vertex, color='green', linestyle='--', linewidth=1.5, alpha=0.7, label=f'对称轴 x = {x_vertex}')

# 绘制最大值水平线
ax.axhline(y=y_vertex, color='orange', linestyle=':', linewidth=1.5, alpha=0.7, label=f'最大值 y = {y_vertex}')

# 绘制坐标轴
ax.axhline(y=0, color='gray', linewidth=0.8)
ax.axvline(x=0, color='gray', linewidth=0.8)

# 求与 x 轴的交点（如果有）
# -2x² + 8x - 3 = 0
# x = (8 ± √(64-24)) / (-4) = (8 ± √40) / (-4)
discriminant = 64 - 24  # b² - 4ac = 64 - 24 = 40
x1 = (8 - np.sqrt(discriminant)) / 4
x2 = (8 + np.sqrt(discriminant)) / 4
ax.plot([x1, x2], [0, 0], 'g^', markersize=10, label=f'与x轴交点')
ax.annotate(f'({x1:.2f}, 0)', xy=(x1, 0), xytext=(x1-0.3, -1.5), fontsize=10, ha='center')
ax.annotate(f'({x2:.2f}, 0)', xy=(x2, 0), xytext=(x2+0.3, -1.5), fontsize=10, ha='center')

# 与 y 轴的交点
y_intercept = f(0)
ax.plot(0, y_intercept, 'ms', markersize=10, label=f'与y轴交点 (0, {y_intercept})')

# 设置坐标轴范围
ax.set_xlim(-1.5, 5.5)
ax.set_ylim(-5, 7)

# 设置网格
ax.grid(True, linestyle='--', alpha=0.5)

# 设置标签和标题
ax.set_xlabel('x', fontsize=14)
ax.set_ylabel('y', fontsize=14)
ax.set_title(r'二次函数 $y = -2x^2 + 8x - 3$ 的图像', fontsize=16, fontweight='bold')

# 添加图例
ax.legend(loc='lower right', fontsize=11)

# 添加关键信息文本框
textstr = '\n'.join([
    r'$y = -2x^2 + 8x - 3$',
    r'$= -2(x-2)^2 + 5$',
    '',
    f'顶点: (2, 5)',
    f'最大值: 5',
    f'对称轴: x = 2'
])
props = dict(boxstyle='round', facecolor='wheat', alpha=0.8)
ax.text(0.02, 0.98, textstr, transform=ax.transAxes, fontsize=11,
        verticalalignment='top', bbox=props)

# 保存图像
plt.tight_layout()
plt.savefig('figure.png', bbox_inches='tight', dpi=150)
plt.close()

print("图像已保存: figure.png")