Questions

• Functions and Graphs Find the maximum and minimum values of quadratic functions by the algebraic method

  給定二次函數 \( f(x) = 2x^2 - 8x + c \)，如果函數的最小值是 -10，求 \( c \) 的值。

  2024

• Exponential and Logarithmic Functions Understand the definitions of rational indices

  簡化表達式 \(\left( 27^{\frac{2}{3}} \cdot 81^{-\frac{1}{4}} \right)\)。

  2024

• Exponential and Logarithmic Functions Understand the definitions of rational indices

  如果 \( x^{\frac{3}{2}} = 27 \)，那麼 \( x \) 的值是多少？

  2024

• Exponential and Logarithmic Functions Understand the laws of rational indices

  簡化下列表達式，並用正指數表示你的答案：\(\frac{8x^{-2}y^3}{2x^{-4}y^{-1}}\)

  2024

• Exponential and Logarithmic Functions Understand the laws of rational indices

  簡化表達式 \((27^{1/3} \cdot 9^{1/2})^6\)。

  2024

• Exponential and Logarithmic Functions Understand the laws of rational indices

  簡化表達式 \((27^{1/3} \cdot 9^{1/2})^6\)。

  2024

• Exponential and Logarithmic Functions Understand the properties of exponential functions and logarithmic functions and recognize the features of their graphs

  考慮指數函數 \( f(x) = 2^x \) 及其對應的對數函數 \( g(x) = \log_2(x) \)。以下關於這些函數的敘述哪一個是真的？

  2024

• Exponential and Logarithmic Functions Solve exponential equations and logarithmic equations

  解指數方程式：\(2^{2x} - 5 \cdot 2^x + 6 = 0\)

  2024

• Exponential and Logarithmic Functions Solve exponential equations and logarithmic equations

  解以下指數方程式找出 \( x \) 的值：\[ (2^2)^x + 3(2^x) + 2 = 0 \]

  2024

• Exponential and Logarithmic Functions Appreciate the applications of logarithms in real-life situations

  地震的強度是參考強度（\(10^{-4}\)）的10,000倍。使用里氏規模公式\(M = \log(\frac{I}{10^{-4}})\)，計算此次地震的震級。

  2024