Functions

symmetry

A property of a graph in which it matches itself after a reflection or rotation.（對稱性；圖形經反射或旋轉後能與原圖重合的性質）

increasing

On an interval, larger input values give larger output values.（遞增；在某區間內，輸入值越大，輸出值也越大）

decreasing

On an interval, larger input values give smaller output values.（遞減；在某區間內，輸入值越大，輸出值越小）

negative

Having output values below zero: f(x) < 0. The graph is below the x-axis for those inputs.（函數值為負；f(x) < 0，對應的圖形位於 x 軸下方）

domain

The set of all input values for which a function is defined.（定義域；使函數有定義的所有輸入值所成的集合）

range

The set of all output values that a function actually produces.（值域；函數實際產生的所有輸出值所成的集合）

extrema

The maximum and minimum values of a function, either locally or over its entire domain.（極值；函數的局部或整個定義域上的最大值與最小值）

square roots

Numbers that, when squared, equal a given number.（平方根；平方後等於某個給定數的數）

factoring

Rewriting an expression as a product of simpler expressions called factors.（因式分解；將式子改寫成較簡單因式的乘積）

quadratic formula

The formula x = (-b ± √(b² - 4ac))/(2a), used to solve ax² + bx + c = 0 when a ≠ 0.（一元二次方程式公式解；當 a ≠ 0 時，用來求 ax² + bx + c = 0 的解）

completing the square

Rewriting a quadratic expression as a squared binomial plus or minus a constant, often to solve an equation or find vertex form.（配方法；將二次式改寫成二項式的平方再加減常數，以解方程式或改寫為頂點式）

vertex form

The form y = a(x - h)² + k, where a ≠ 0 and (h, k) is the vertex of the parabola.（頂點式；y = a(x - h)² + k，其中 a ≠ 0，頂點為 (h, k)）

vertex

The turning point of a parabola, where the function has its minimum or maximum value.（頂點；拋物線的轉折點，也是函數取得最小值或最大值的位置）

discriminant

The expression b² - 4ac in a quadratic equation with real coefficients: positive means two distinct real solutions, zero means one repeated real solution, and negative means no real solutions.（判別式 b² - 4ac；實係數二次方程式中，大於零有兩個相異實根，等於零有重根，小於零沒有實根）