73 lines
1.5 KiB
Python
73 lines
1.5 KiB
Python
# /// script
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# requires-python = ">=3.11"
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# dependencies = ["numpy", "matplotlib"]
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# ///
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import numpy as np
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import matplotlib.pyplot as plt
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# 设置中文字体
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plt.rcParams["font.sans-serif"] = [
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"WenQuanYi Micro Hei",
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"Noto Sans CJK SC",
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"Microsoft YaHei",
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"SimHei",
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"SimSun",
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"DejaVu Sans",
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]
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plt.rcParams["axes.unicode_minus"] = False
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# 定义函数
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def f(x):
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return -2 * x**2 + 8 * x - 3
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# 顶点坐标
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x_vertex = 2
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y_vertex = 5
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# 生成 x 值（根据顶点位置合理设置范围）
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x = np.linspace(0.5, 3.5, 400)
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y = f(x)
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# 绘图
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plt.figure(figsize=(10, 7), dpi=150)
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# 绘制函数曲线
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plt.plot(x, y, "b-", linewidth=2, label="y = -2x² + 8x - 3")
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# 标记顶点
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plt.plot(
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x_vertex, y_vertex, "ro", markersize=10, label=f"顶点 ({x_vertex}, {y_vertex})"
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)
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# 添加顶点坐标标注
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plt.annotate(
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f"最大值\n({x_vertex}, {y_vertex})",
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xy=(x_vertex, y_vertex),
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xytext=(2.5, 3),
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arrowprops=dict(arrowstyle="->", color="red", lw=1.5),
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fontsize=10,
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color="red",
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)
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# 添加坐标轴标签和标题
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plt.xlabel("x", fontsize=12)
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plt.ylabel("y", fontsize=12)
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plt.title("二次函数 y = -2x² + 8x - 3 的图像", fontsize=14, pad=15)
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# 设置坐标轴范围
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plt.xlim(0.5, 3.5)
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plt.ylim(0, 6)
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# 显示网格
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plt.grid(True, alpha=0.3, linestyle="--")
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# 添加图例
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plt.legend(loc="upper right", fontsize=10)
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# 保存图像
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plt.savefig("figure.png", bbox_inches="tight")
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print("图像已保存: figure.png")
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