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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).

Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

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.

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.

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Factor a quadratic expression to reveal the zeros of the function it defines.

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. Graph linear and quadratic functions and show intercepts, maxima, and minima.

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.