Quadratic and Exponential Equations and Functions
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Use the process of factoring to determine zeros, lines of symmetry, and extreme values in real-world and other mathematical problems involving quadratic functions; interpret the results in the real-world contexts.
Represent real-world and other mathematical problems that can be modeled with exponential functions using tables, graphs, and equations of the form y = abˣ (for integer values of x > 1, rational values of b > 0 and b ≠ 1); translate fluently among these representations and interpret the values of a and b.
Solve quadratic equations in one variable by inspection (e.g., for x² = 49), finding square roots, using the quadratic formula, and factoring, as appropriate to the initial form of the equation.
Represent real-world problems using quadratic equations in one or two variables and solve such problems with and without technology. Interpret the solution and determine whether it is reasonable.
Describe the relationships among the solutions of a quadratic equation, the zeros of the function, the x-intercepts of the graph, and the factors of the expression.