Completing the Square N-CN.7 Solve quadratic equations with real coefficients that have complex solutions. A-SSE.3 Choose and produce an equivalent form.

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Presentation transcript:

Completing the Square N-CN.7 Solve quadratic equations with real coefficients that have complex solutions. A-SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. A-REI.4 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 x 2 = 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. G-GPE.1 Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.

Solving Using Square Roots

Completing the Square

Solving by Completing the Square

Standard Form of a Circle