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Algebra 2 – Chapter 5 Quadratics • Homework: • page 245 (1-19, 33-37) odd 5-2 Properties of Parabolas maximum or minimum • homework: • graphing worksheet • find a photo of a parabolic structure and find the quadratic equation represented by it. • Present you answer as a poster with the object and showing how you worked out the equation. 5-4 Factoring Quadratic Expressions EQ: How do you reduce a quadratic expression into its linear factors? • Warm Up: • Factor these expressions – Algebra 1 Review – Do you remember? 5-4 Factoring Quadratic Expressions EQ: How do you reduce a quadratic expression into its linear factors? • Factoring is rewriting an expression as the product of its factors. • The greatest common factor (GCF) of the expression is a common factor of the term of the expression. 5-4 Factoring Quadratic Expressions EQ: How do you reduce a quadratic expression into its linear factors? • When you factor a quadratic expression in the form ax2 + bx +c you are looking for a pair of factors that multiply to equal ac and add to equal b. 5-4 Factoring Quadratic Expressions EQ: How do you reduce a quadratic expression into its linear factors? 5-4 Factoring Quadratic Expressions EQ: How do you reduce a quadratic expression into its linear factors? 5-4 Factoring Quadratic Expressions EQ: How do you reduce a quadratic expression into its linear factors? 5-4 Factoring Quadratic Expressions EQ: How do you reduce a quadratic expression into its linear factors? • Homework: page 268 (1-45) every other odd Simplifying Square Roots Simplifying Square Roots • Break the number in the radical down to its prime factors – use a factor tree or repeated division. • 72 = 9 ∙ 8 = 3 ∙ 3 ∙ 4 ∙ 2 = 3 ∙ 3 ∙ 2 ∙ 2 ∙ 2 • Each pair of factors represents a single root that you can solve out of the radical • √3∙3∙2∙2∙2 =3∙2√2=6√2 Simplifying Square Roots • Process is true for variables as well • Every pair of variables represents a single root variable • √ b3 = b √ b 5-6 Complex Numbers How do you take the square root of a negative number? • Up until now, there was no way to deal with a root like this: √ -25. • The letter i is defined as the square root of negative 1, and can be simplified out of a square root. • The numeral is rationalized the same way. • √ -25 = √ -1 ∙25 = i √ 25 = 5i 5-6 Complex Numbers How do you take the square root of a negative number? 5-6 Complex Numbers How do you take the square root of a negative number? • Use the Complex Number Plane to represent a complex number geometrically. • Locate the real part of the complex number on the horizontal axis and the complex part on the vertical axis. 5-6 Complex Numbers How do you take the square root of a negative number? • The absolute value of a complex number is its distance from the origin in the complex number plane. • You can find the absolute value by using the Pythagorean Theorem. 5-6 Complex Numbers How do you take the square root of a negative number? • When you add or subtract complex numbers you combine the real parts and imaginary parts separately. • When you multiply complex numbers you use the rules for multiplying binomials (FOIL) • Remember that i2 = -1 5-6 Complex Numbers How do you take the square root of a negative number? 5-6 Complex Numbers How do you take the square root of a negative number? 5-6 Complex Numbers How do you take the square root of a negative number? • Exit Pass – write answers in a + bi form homework: p 282 (1-35) odd, (39-44) all 5-7 Completing the Square Using perfect squares to solve equations • Warm Up: 5-7 Completing the Square Using perfect squares to solve equations 5-7 Completing the Square Using perfect squares to solve equations 5-7 Completing the Square Using perfect squares to solve equations 5-7 Completing the Square Using perfect squares to solve equations 5-7 Completing the Square Using perfect squares to solve equations 5-7 Completing the Square Using perfect squares to solve equations 5-7 Completing the Square Using perfect squares to solve equations 5-7 Completing the Square Using perfect squares to solve equations • homework: page 289 (1-33) odd • Chapter 5 study guide will be given out at our next class. • Chapter 5 Test will be given the Tuesday (5th) /Wednesday (4th) after Thanksgiving break. 5-8 The Quadratic Formula • Homework: • p 289 (23-33) odd • p 297 (1-39) odd • Chapter 5 test on Wednesday