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Quadratics with complex roots! Do Now: Solve the following Quadratic: y = x 2 -4x + 6 Reminder: Take out pencil, HW on the left corner of your desk, please begin the do-now immediately! Homework: Worksheet HW #2.5 & quadratics worksheet Objectives: Apply the Quadratic Formula and knowledge of real and imaginary numbers to find and simplify roots of any quadratic equation. Use i to simplify square roots of negative numbers Simplify square roots of fractions with denominators

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AGENDA Do Now w/ share (10 min) Simplifying harder square roots (10) Practice (10) Quadratic Equations with complex roots TTG (5) Objective: students will be simplify harder square roots and solve quadratics with complex and real roots.

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Simplifying hard square roots Three golden rules of radicals 1. Never leave a perfect square under a radical (even if it is embedded in another number (i.e. 40) 2. Never leave a negative number under the radical (use i) 3. Never leave a radical in the denominator of a fraction Objective: students will be simplify harder square roots and solve quadratics with complex and real roots.

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Simplifying Radicals cont. How do you simplify radicals when there are fractions Separate the numerator and denominator into two radicals Simplify each part Reduce whole number part if possible If there is still a radical in the denominator there is 1 more step!!! multiply numerator and denominator by that radical. Let’s try it! Objective: students will be simplify harder square roots and solve quadratics with complex and real roots.

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Solving Quadratic Equations Solve and simplify: y = 2x 2 – 4x + 3 Start HW! Objective: Objective: students will be simplify harder square roots and solve quadratics with complex and real roots.

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