# 頂點 (曲線)

（重定向自頂點 (事物)

## 圓錐曲線的頂點

### 拋物線的頂點

${\displaystyle f(x)=ax^{2}+bx+c}$
${\displaystyle {\frac {\mathrm {d} f(x)}{\mathrm {d} x}}=2ax+b}$
${\displaystyle 2ax+b=0\leftrightarrow x=-{\frac {b}{2a}}}$

## 參考文獻

1. Agoston, Max K., Computer Graphics and Geometric Modelling: Mathematics, Springer, 2005, ISBN 9781852338176
2. Gibson, C. G., Elementary Geometry of Differentiable Curves: An Undergraduate Introduction, Cambridge University Press, 2001, ISBN 9780521011075
3. Fuchs, D. B.; Tabachnikov, Serge, Mathematical Omnibus: Thirty Lectures on Classic Mathematics, American Mathematical Society, 2007, ISBN 9780821843161
4. ^ Apostol, Tom M.; Mnatsakanian, Mamikon A., New Horizons in Geometry, The Dolciani Mathematical Expositions #47, The Mathematical Association of America: 251, 2012, ISBN 978-0-88385-354-2
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12. ^ Routh, Edward John. Chapter X: On Strings. A Treatise on Analytical Statics. University Press. 1891.
13. ^ Agoston, Computer Graphics and Geometric Modelling: Mathematics, 2005,[1] Theorem 9.3.9, p. 570
14. ^ Gibson, Elementary Geometry of Differentiable Curves: An Undergraduate Introduction, 2001,[2] Section 9.3, "The Four Vertex Theorem", pp. 133–136
15. ^ Fuchs, D. B.; Tabachnikov, Serge, Mathematical Omnibus: Thirty Lectures on Classic Mathematics, 2007,[3] Theorem 10.3, p. 149.
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17. ^ Ghomi, Mohammad, Boundary torsion and convex caps of locally convex surfaces, 2015, Bibcode:2015arXiv150107626G, arXiv:1501.07626
18. ^ 【頂點】. 教育部重編國語辭典修訂本.
19. ^ R.A.约翰逊，单墫 译. 《近代欧氏几何学》. 上海教育出版社. ISBN 7-5320-6392-5.