ALGEBRA 2 – CHAPTER 5 QUADRATICS. ANGRY BIRDS! Angry Birds follow a parabolic path. Your quest is...

ALGEBRA 2

– CHAPT

ER 5Q U A D R A T I C S

ANGRY BIRDS!Angry Birds follow a parabolic path. Your quest is to find the

equation of the parabola to cause the angry bird to hit the pig. Use the given information and the quadratic regression method to find the equation of the curve.

All numbers are decimals – round to the thousandths place.

When you think your answer is correct, bring it to me to check it on the computer. Groups that successfully find all four equations will earn a prize. (woooo!)

Homework:

page 245 (1-19, 33-37) odd

5-2 PROPERTIES OF PARABOLAS

MAXIMUM OR MINIMUM

homework:

5-4 FACTORING QUADRATIC EXPRESSIONS

EQ: HOW DO YOU REDUCE A QUADRATIC EXPRESSION INTO ITS LINEAR FACTORS?

Factor these expressions – Algebra 1 Review – Do you remember?



• 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.



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.



Homework: page 268 (1-45) every other odd

5-4 SOLVING QUADRATIC EQUATIONSSolving a quadratic equation means finding the values of

the variable that make the equation true.

Usually, for a quadratic equation, there are two solutions.

There are several methods to solve quadratic equations:

• Factoring

• Finding Square Roots

• Completing the Square

• Using the Quadratic Formula

5-4 SOLVING QUADRATIC EQUATIONSSolving by factoring requires:

Setting the equation equal to zero

Completely factoring the equation

Using the Zero-Product property to find the zeros.

Set each factor equal to zero and solve for the variable. This solution is called a zero of the equation because it makes the equation equal zero.

ZERO PRODUCT PROPERTY: If ab = 0 then a = 0 or b = 0

Example: if then

5-4 SOLVING QUADRATIC EQUATIONS

Standard Form for a Quadratic Equation:

ZERO PRODUCT PROPERTY: If ab = 0 then a = 0 or b = 0

Example: if then

5-4 SOLVING QUADRATIC EQUATIONSUse factoring to solve the following equations:

5-4 SOLVING QUADRATIC EQUATIONSSolving by finding Square Roots is used when there is no

linear term.

• Rewrite equation as

• Isolate

• Find square roots (remember, there are two!)

• Example:

Try These:

SIMPLIFYING SQUARE ROOTS

√𝑎𝑏=√𝑎 ∙√𝑏 =

¿ 4√3

𝑆𝑖𝑚𝑝𝑙𝑖𝑓𝑦 √ 48√ 48=√16 ∙√3


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

= 6


Process is true for variables as well

Every pair of variables represents a single root variable

=

5-6 COMPLEX NUMBERSHOW DO YOU TAKE THE SQUARE ROOT OF A NEGATIVE NUMBER?

Up until now, there was no way to deal with a root like this:

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 in the usual way

=


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.


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.

Find the absolute value:


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


Write each answer in a + bi form

5-7 COMPLETING THE SQUARE

USING PERFECT SQUARES TO SOLVE EQUATIONS

5-7 COMPLETING THE SQUARE

USING PERFECT SQUARES TO SOLVE EQUATIONS

You can solve an equation where one side of the equation is a perfect square by finding square roots.

5-7 Completing the SquareUsing perfect squares to solve equations

If one side of an equation is not a perfect square, you can rewrite the constantterm to get a perfect square trinomial.Use this relationship to complete the square:

𝒙𝟐+𝟏𝟎𝒙+¿


Find the missing constant to complete the square: write the factored square.

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 Thursday(5th) and Friday (6th) after Thanksgiving break.


5-8 THE QUADRATIC FORMULA

Homework:

p 289 (23-33) odd

p 297 (1-39) odd

ALGEBRA 2 – CHAPTER 5 QUADRATICS. ANGRY BIRDS! Angry Birds follow a parabolic path. Your quest is...

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