Quadratics

Math makes life accurate

What is a Quadratic Equation?

An equation where the highest power of an unknown exponent which is usually "X" is a square.

Parts of the Parabola

How to plot a Graph

This video shows how to plot a point on a graph paper. This skill will be required later on in the lesson.
How to Plot on Graph Paper : Easy-to-Intermediate Math

Writing Equations from Quadratic Table of Values

Writing Equations from Quadratic Tables

Word Problem

How to identify if an equation is Linear, Quadratic or Exponential using finite differences.

How to Tell if a Table is Linear, Quadratic, or Exponential
This picture shows that quadratic equations have a constant second difference.

Transformations of Quadratics

Understanding this concept will help in graphing a parabola

Memorizing these transformations can make the quadratics unit easy for you.

How to graph using Quadratic Transformations

4.1 Quadratic Functions - Transformations

Word Problem

How to write an equation in vertex form using a graph

writing equation vertex form solving a

Graphing using Factored Form y = a(x-r) (x-s)

This videos shows how to find the roots, direction of opening, axis of symmetry and vertex of an equation and then graph it.
Graphing Parabolas in Factored Form y=a(x-r)(x-s)

Word Problem

How to determine an Equation from a Parabola in y=a(x-r) (x-s) Factored Form

Factored Form (Determining an equation from a graph)

Multiplying Polynomials

Using distributive property

Algebra I Help: Multiplying Polynomials

Word Problem

Using FOIL method

Algebra I Help: FOIL (Method for Multiplying two Binomials)

Special Cases

There can be two types of special cases in multiplying polynomials

  • Difference of Squares
  • Perfect Square

A110.4 Multiplying Polynomials Special Cases

Factoring

Common Factoring

Polynomial Factoring The Greatest Common Factor (GCF)

Factoring by Grouping

Factoring by Grouping
Example of Factoring by Grouping

Word Problem

Standard Form (x^2+bx+c) to Factored Form

How to Factor Quadratic Expressions

Standard Form (ax^2+bx+c) to factored form

Algebra I Help: Factoring Trinomials of the Form ax^2+bx+c Part III

Word Problem

Special Cases

Just like in expanding, there are two special cases in factoring as well

  • Difference of Squares
  • Perfect Square


Factoring Special Cases

Word Problem

Review for Factoring

Quadratic Formula

This formula might look complicated but it is very easy

maxima and minima

How to write Standard Form into Vertex Form (Completing the Square)

Changing a Quadratic from Standard Form to Vertex Form

Word Problem

Solving Quadratic Equation (x-r) (x-s)=0

Solving Quadratic Equation x^2+bx=c

"C" must be shifted to the other side along with x^2+b and must equal to zero

For instance - x^2+3x = 6 will then be written as x^2+3x-6=0

Word Problem

Find the X-Intercepts by Factoring a Quadratic Equation

Quadratic equation : Find x-intercepts by factoring

How to graph using the X-intercepts

Graph Quadratics Using the x-Intercepts Part 1

How to solve Equations using the Quadratic Formula

How to Solve Quadratic Equations

Discriminant of a Quadratic Equation

Discriminant of Quadratic Equations

Easy way to know the number of solutions you will get for an equation

Video on Factoring

By - Taran
https://www.youtube.com/watch?v=R_oolbgxNfQ

How can all the above lessons be used in one Word Problem (Linking all the topics)

This word problem will use all the quadratic topics in one.

Assessment

Reflection on the Quadratics Unit

The quadratics unit was as hard as I was told from my peers that took Math last semester. Even though there were many ups and downs with which I had to struggle with in the unit. The Quadratics unit was divided into three parts, each part had its own level of difficulty. In the first part of Quadratics Unit we were taught about graphing parabolas and how to write equations in Vertex Form. The first unit was fairly easy compared to the other two parts. On the unit test I scored 80%, which I think is a good mark but it can be improved. In the second Quadratics Unit we were taught Expanding and Factoring Trinomials using many different ways like distributive method, FOIL method, Factoring by Grouping and using special cases. We also learned how to change standard form to factored form. Even though the unit was very basic I still struggled a lot with Factoring and Application problems, and I was also unable to perform well on the Unit Test. The third part of the Quadratics was a lot of fun because we were introduced to the Quadratic Formula which is very easy. The method of Completing the square was also very interesting because it was something that I never knew about and I never thought that this component of math will be this easy. This unit had an intermediate level of difficulty. The unit test for Quadratics Part 3 was easy compared to the other two unit tests, but I think I made a mistake in one of the questions. Even though Quadratics was a difficult unit, but I learned a lot of different ways to solve an equation and it was also an introduction to parabolas which I was unaware about in Grade 9. The best part about this unit is the Smore Assignment because it is a great way to bring up the marks in math class. This assignment is a great opportunity to me because I was disappointed with my marks in quadratics part 2 unit test, and I think this assignment is going to help me to a great deal.

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