Transcript A2 Ch 5 Quadratics Lecture Notes

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