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Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. Rewrite expressions involving radicals and rational exponents using the properties of exponents.

Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. Rewrite expressions involving radicals and rational exponents using the properties of exponents.

Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. Rewrite expressions involving radicals and rational exponents using the properties of exponents.

Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. Solve quadratic equations with real coefficients that have complex solutions.

Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, factoring, completing the square, and the quadratic formula, as appropriate to the initial form of the equation (limit to real number solutions).

Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. Solve quadratic equations with real coefficients that have complex solutions.

Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, factoring, completing the square, and the quadratic formula, as appropriate to the initial form of the equation (limit to real number solutions).