形狀與它的鏡像線
[[quadratic-function|二次函數]] f(x) = a x^2 + b x + c 的圖形是一條[[parabola|拋物線]]，一條光滑的 U 形曲線。若 a > 0，U 形開口向上；若 a < 0，開口向下。拋物線關於一條豎直線完全對稱，這條線叫做[[axis-of-symmetry|對稱軸]]；而曲線轉向的那個唯一的點——最低點或最高點——就是[[vertex|頂點]]，它恰好落在對稱軸上。
Axis of symmetry of f(x) = a x^2 + b x + c:
x = -b / (2a)
Find the vertex of f(x) = x^2 - 4x + 1:
x = -(-4) / (2·1) = 4/2 = 2 (axis: x = 2)
f(2) = 2^2 - 4·2 + 1 = 4 - 8 + 1 = -3
Vertex = (2, -3), opens upward (a = 1 > 0)
so the minimum value of f is -3.頂點式一眼看出頂點
同一條拋物線也可以寫成[[vertex-form|頂點式]] f(x) = a(x - h)^2 + k，其中頂點就是 (h, k)。你可以透過配方法從標準形式得到它。頂點式是拋物線最直白的 X 光片：h 把它左右平移，k 把它上下平移，而 a 仍然控制開口的寬窄和朝向。
Rewrite f(x) = x^2 - 4x + 1 in vertex form:
f(x) = (x^2 - 4x) + 1
= (x^2 - 4x + 4) - 4 + 1 (add & subtract (4/2)^2 = 4)
= (x - 2)^2 - 3
Vertex form: f(x) = (x - 2)^2 - 3
Read directly: vertex (h, k) = (2, -3).
Same vertex we found from x = -b/(2a) — they must agree.