ALGEBRA I Unit 10: Quadratic Equations Unit Notes Packet

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Algebra I. Unit 10 Assignments. Section. Topic. Home Work. Due Date. 1. Quadratic Equations. 2. Completing the Square. 3. Quadratic Formula. 4. Functions. 5.
Name:__________________________

Period:_____________

ALGEBRA I

Unit 10: Quadratic Equations Unit Notes Packet

Algebra I Unit 10 Assignments

Section

Topic

1

Quadratic Equations

2

Completing the Square

3

Quadratic Formula

4

Functions

5

Unit 10 Review

Test

Unit 10 Test

Home Work

Due Date

Section 13.1-13.2 Quadratic Equations Vocabulary: 1. Standard Form 2. Quadratic Equation

What is a quadratic equation? 

Remember, __________________________________ means that the degree of the polynomial is _______, being that quadratic comes from the Latin word for ___________________.



________________________________________________ just means an equation whose highest degree term is _______.



If ________ is the only variable we can solve the equation using very familiar steps.

Example 1: Solve for x. a) _______________________ Step 1: ____________________________________

Step 2: ____________________________________

b) ________________________



We learned to solve some quadratic equations in our chapter on factoring. The steps were…

1. Get everything on to one side. 2. Factor 3. Use Principle of Zero Products (Set all factors equal to zero) 4. Solve all equations for x.

What is standard form? 

When we complete the step where we get everything onto one side we are putting the quadratic equation into __________________________________________.



Standard form always looks as follows, ______________________________________________, where a,b, and c are all some constant numbers.

Example 2: Convert the equation into standard form. a) __________________________________________

b) __________________________________________

13.3 Completing the Square Vocabulary: 1. Completing the square



Once you get the equation into standard form you can try to solve for x by ________________ the equation, but if the equation cannot be _________________________ we can use a process called _____________________________________________________________________.

How do you complete the square? Example 3: Solve for x by completing the square. a) _________________________________________ Step 1: _____________________________________

Step 2: ______________________________________  

This step is done by adding a number to both sides. This number is the coefficient of 𝒙 ÷ 𝟐 then squared.

Step 3: _________________________________

Step 4: __________________________________

Step 5: ___________________________________ b) ___________________________________

c) _____________________________________

d) ______________________________________ 

If there is a coefficient of 𝑥 2 , begin the problem by dividing everything by that number.

Section 13.4 Quadratic Formula Vocabulary: 1. Quadratic Formula 

From the process of _______________________________________ mathematicians were able to take the formula for _____________________________________________________ and solve for ______ (See page 589), giving us a new formula.



This new formula called the _____________________________________________ is a way of using the values of ____, ____, and ____ to calculate the values for x.

Example 1: Solve using the quadratic formula. a) _______________________

b) _______________________

c) _______________________

Chapter 12 Functions Vocabulary: 1) Relation 2) Domain 3) Range 4) Function 5) Vertical Line Test

What is a relation? 

A _________________________ is a set of _____________________________________ where ____ is the first member or coordinate and ____ is the second coordinate.



Remember from chapter 9 that _______ are always denoted or grouped with _____________________.



The ________________ of a relation is the set of all of its ___________ coordinates.



The ________________ of a relation is the set of all of its ___________ coordinates.

What is a function? 

Like _____________________________________, a ___________________________ is a specific calculation that matches ________ value from the domain of a relation with exactly _________ value from the range of that relation.



In other words, each member of the ______________________ has only __________ value paired to it.

How do you know if a relation is a function?



In order to determine if a relation is a function or not, check to make sure that each x coordinate has only _________ y coordinate paired to it.

Example 1: Determine whether each relation is a function or not. a) _____________________________________________________

b) _____________________________________________________

c) _____________________________________________________

How do you know if a graph is a function? 

To determine if a graph is a function we use the _________________________________________.



If it is possible for a ____________________________ to intersect a graph at more than one point, then the graph is ________________________________.

Example 2: Determine whether the graph is a function or not.

a)

B)

c)

d)

How do we use functions?



When given a function ___________we can _________________________________ in order to find the ______________________________________.

Example 3:

a) _________________________

b) ______________________

_________

_________

_________

_________

__________

__________

How do we find the domain of a function? 

When finding the domain of a function f(x) we need to find out what ____________________ x cannot be.



Primarily we will see examples where we will use the rule, that you cannot divide by 0.

Example 4: Find the domain of f(x). a) _________________________

b) ________________________