01-基石题-test

01-基石题-test/工具GithubCopilot模型gemini-claude-opus-4-5-thinking/plot.py

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+# /// 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")