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16 Days

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Two Days

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Review - Use FOIL and the Distributive Property to multiply polynomials.

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Writing a polynomial as a product of its factors. Essentially undoing the multiplication. Purposes of factoring: ◦ Simplifying ◦ Rewriting ◦ Solving

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GCF

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Grouping

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Difference of Squares

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Difference of Squares Formula

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Perfect Square Trinomials

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Perfect Square Trinomial Formulas

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Trinomials (a=1)

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Trinomials (a≠1)

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Sum and Difference of Cubes Formulas

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Sum and Difference of Cubes

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pg 263 (# 2-30 even)

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Two Days

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Question: How can we multiply two or more numbers together and get a product that equals zero? For any real numbers a and b, if ab=0, then either a=0, b=0, or both.

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The solutions are -3 and 1/2.

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Factor using “difference of two squares.”

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Did you take out GCF?

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1. 1. 2. 2. 3. 3. 4. 4. 5. If all are correct, you’re finished! 5.

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Back to questions

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One Day

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Two Days

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Solve the following quadratic:

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The Imaginary Unit (i) has the following properties. The imaginary number i is defined as the number whose square is -1. That is: Imaginary Numbers are of the form a + bi where b ≠ 0. Complex Numbers are of the form a + bi where a and b are Real Numbers.

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We can add and subtract imaginary numbers similar to how we add and subtract terms with variables. Think “like terms.”

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Similarly, we can multiply imaginary numbers following the same exponent rules we use for variables.

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The absolute value of a complex number is the distance the number lies from the origin in the complex plane. Think Pythagorean Thm..

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Larger powers of i can be simplified by dividing the power by 4 and using the remainder to determine the appropriate value.

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Solve:

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Pg 278 (# 1-45 odd)

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If z = a + bi is an imaginary number, the its conjugate is z = a – bi. Complex Conjugates can be used to eliminate imaginary numbers from the denominators of fractions. This is very similar to how we rationalize denominators.

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Eliminate the Imaginary numbers from the denominator in the following example.

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Practice 5-6 WS (even)

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Two Days

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l Examples l x 2 + 6x + 9 l x 2 - 10x + 25 l x 2 + 12x + 36

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l In the following perfect square trinomial, the constant term is missing. X 2 + 14x + ____ l Find the constant term by squaring half the coefficient of the linear term. l (14/2) 2 X 2 + 14x + 49

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Solve the following using the quadratic formula: What do we notice about these two problems? How else could we Have solved these quadratics?

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Solve the following quadratics:

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pg 293 (# 1-29 odd)

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1 Day

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1.When you solve using completing the square on the general formula you get: 2.This is the quadratic formula! 3.Just identify a, b, and c then substitute into the formula.

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The quadratic formula allows you to solve ANY quadratic equation, even if you cannot factor it. An important piece of the quadratic formula is what’s under the radical: b 2 – 4ac This piece is called the discriminant.

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The discriminant tells you the number and types of answers (roots) you will get. The discriminant can be +, –, or 0 which actually tells you a lot! Since the discriminant is under a radical, think about what it means if you have a positive or negative number or 0 under the radical.

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Value of the DiscriminantNature of the Solutions Negative2 imaginary solutions Zero1 Real Solution Positive – perfect square2 Reals- Rational Positive – non-perfect square 2 Reals- Irrational

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Pg 293 (#31-39 odd) Practice 5-8 WS (#2-26 even) Quiz 5.8 on 11/18!!

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1 Day

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The standard form of a quadratic is

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The graph of a quadratic function is called a parabola. The axis of symmetry is the vertical line that divides the parabola into two identical halves and is written x=a. The vertex (a,b) of the parabola is the point at which the parabola intersects the axis of symmetry and is also a maximum or minimum point of the function.

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Given 3 points on the function we can determine the equation of the quadratic.

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pg. 241 (#1-12 all, 21)

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4 Days

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3 Days

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Standard form of a Quadratic: Vertex form of a Quadratic:

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