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

import numpy as np
import matplotlib.pyplot as plt

# 设置字体
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
def f(x):
    return -2*x**2 + 8*x - 3

# 生成 x 数据（根据顶点位置设置合理范围）
x = np.linspace(-1, 5, 500)
y = f(x)

# 绘制函数曲线
ax.plot(x, y, 'b-', linewidth=2.5, label=r'$y = -2x^2 + 8x - 3$')

# 标记顶点
vertex_x, vertex_y = 2, 5
ax.scatter([vertex_x], [vertex_y], color='red', s=120, zorder=5, edgecolors='darkred', linewidths=2)
ax.annotate(f'顶点 ({vertex_x}, {vertex_y})\n最大值',
            xy=(vertex_x, vertex_y),
            xytext=(vertex_x + 0.8, vertex_y + 0.5),
            fontsize=12,
            ha='left',
            arrowprops=dict(arrowstyle='->', color='red', lw=1.5),
            bbox=dict(boxstyle='round,pad=0.3', facecolor='lightyellow', edgecolor='orange'))

# 标记与 x 轴的交点（求根）
# -2x² + 8x - 3 = 0 → x = (8 ± √(64-24))/(-4) = (8 ± √40)/(-4)
discriminant = 64 - 24
x1 = (8 - np.sqrt(discriminant)) / 4
x2 = (8 + np.sqrt(discriminant)) / 4
ax.scatter([x1, x2], [0, 0], color='green', s=100, zorder=5, marker='s', edgecolors='darkgreen', linewidths=2)
ax.annotate(f'x ≈ {x1:.2f}', xy=(x1, 0), xytext=(x1 - 0.3, -1.5), fontsize=10, ha='center',
            arrowprops=dict(arrowstyle='->', color='green', lw=1))
ax.annotate(f'x ≈ {x2:.2f}', xy=(x2, 0), xytext=(x2 + 0.3, -1.5), fontsize=10, ha='center',
            arrowprops=dict(arrowstyle='->', color='green', lw=1))

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

# 绘制参考线
ax.axhline(y=0, color='gray', linestyle='-', linewidth=0.8, alpha=0.5)
ax.axhline(y=vertex_y, color='orange', linestyle=':', linewidth=1.5, alpha=0.7, label=f'最大值 y = {vertex_y}')

# 填充顶点到 x 轴的区域（可视化最大值）
x_fill = np.linspace(x1, x2, 100)
y_fill = f(x_fill)
ax.fill_between(x_fill, y_fill, 0, alpha=0.15, color='blue', label='函数值 > 0 的区域')

# 设置坐标轴
ax.set_xlim(-1, 5)
ax.set_ylim(-4, 7)
ax.set_xlabel('x', fontsize=14)
ax.set_ylabel('y', fontsize=14)
ax.set_title(r'二次函数 $y = -2x^2 + 8x - 3$ 图像', fontsize=16, fontweight='bold')

# 添加网格
ax.grid(True, linestyle='--', alpha=0.4)

# 添加图例
ax.legend(loc='lower right', fontsize=11, framealpha=0.9)

# 添加说明文字框
textstr = '\n'.join([
    '关键信息:',
    f'• 顶点坐标: ({vertex_x}, {vertex_y})',
    f'• 最大值: {vertex_y}',
    f'• 开口方向: 向下 (a < 0)',
    f'• 对称轴: x = {vertex_x}'
])
props = dict(boxstyle='round', facecolor='white', edgecolor='gray', alpha=0.9)
ax.text(0.02, 0.98, textstr, transform=ax.transAxes, fontsize=11,
        verticalalignment='top', bbox=props)

plt.tight_layout()
plt.savefig('figure.png', bbox_inches='tight', facecolor='white')
plt.close()

print("图像已保存: figure.png")