Students add, subtract, multiply, divide, reduce and evaluate rational expressions with monomial and polynomial denominators, and simplify complicated fractions including fractions with negative exponents in the denominator. Students solve and graph quadratic equations by factoring, completing the square, or using the quadratic formula. Students apply these techniques in solving word problems. They also solve quadratic equations in the complex number system. Students demonstrate and explain the effect changing a coefficient has on the graph of quadratic functions.
Students graph quadratic functions and determine the maxima, minima, and zeros of the function.
Students prove simple laws of logarithms. 11.1 Students understand the inverse relationship between exponents and logarithms, and use this relationship to solve problems involving logarithms and exponents. Students judge the validity of an argument based on whether the properties of real numbers, exponents, and logarithms have been applied correctly at each step. Students know the laws of exponents, understand exponential functions, and use these functions in problems involving exponential growth and decay. Students use the definition of logarithms and the product formula for logs to translate between logarithms in any bases.