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Solve quadratic equations in one variable.

Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)2 = q that has the same solutions. Derive the quadratic formula from this form.

Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

Solve quadratic equations with real coefficients that have complex solutions. Solve quadratic equations in one variable.

Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

Find inverse functions. Produce an invertible function from a non-invertible function by restricting the domain.

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

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).

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).