# Quadratic Unit Assignment

### By:Tharakaa Rajakumar

## Definition Of Quadratics:

**meaning square because the variable gets squared. Quadratics is also used in our everyday life.**

__Quad__## Table Of Contents

__Introduction__

**1. Quadratic Relations**

**Second differences**

**2. Introduction To Parabola**

**Parabola's Labels****The Parabolic****Definitions**

**3. Transformations Of Quadratics**

**The Base****The Step Pattern**

**Types Of Equations**

**1. Factored Form**

**Expanding/Distributive Property to Standard Form****Difference of Squares****Perfect Squares****Graphing Factored Form****Common Factoring****Factoring Simple Trinomials to Standard Form**

**2. Standard Form**

**Completing The Square Standard Form To Vertex Form****Grouping Standard form to Factored form****Complex trinomials standard form to factored form****Quadratic Formula****Discriminant**

**3. Vertex Form**

**Graphing Vertex Form****Solving For X****Solving For Y**

**Word Problems**

**Optimization questions**

**Connection To All The Quadratic Parts and ****Reflection**

## Types of Quadratic Equations

**1. Vertex Form: y=a(x-h)² + k**

** 2. Factored Form: y=a(x-r) (x-s)**

**3. Standard Form: y=ax² + bx + c**

## Quadratic Relations Using Second Differences

## Defintion of Parabolic Terms

**1. Vertex-**The vertex can be the maximum or the minimum of the parabola depending on the direction of the opening. If the parabola open downward then it will have a maximum value (Highest Point). If the parabola opens upward then it will have a minimum value (Lowest Point).

**2. Axis of Symmetry-** Is the line that divides the parabola into two symmetric portions

3. **X-intercepts-** Points on the graph that intercept the x-axis.

4. **Y-intercepts-** Points on the graph that intercept the y-axis

5. **Optimal Value-** Highest y-value of a parabola.

## The Step Pattern

## The Transformations

## Factored Form

## Expanding/ Distributive Property

**There are two ways to do Expanding In Factored Form to Standard Form in distributive property.**

**1. Simple distributive property is used when there's only a variable like x with no coefficients in front **

**2. FOIL in expanding for when there is a coefficient beside the variable x.**

** F- First**

** O-Outer**

** I-Inner**

** L-Last**

Ex.1 (6x +1) (x-3)

** F- (6x) (x) = 6x****²**

** O- (6x) (-3)= -18x**

** I- (1) (x) = x**

** L-(1) (-3) =-3**

**= 6x² -17x-3**

## Perfect Squares

## Perfect Square Algebra Tiles Since all the the tiles fit the equation is a perfect square. | ## Perfect Square Algebra Tiles Since all the the tiles fit the equation is a perfect square. | ## How to factor a perfect square |

## Difference Of Squares

a² - b² or (9x+8y) (9x-8y)

= 81x² - 72xy + 72xy - 64y²

= 81x² - 64y²

The (9x) multiplies with the other (9x) which becomes (81) and then the two (x's) square and as a total becoming (81x²). Then the (9x) multiplies with the (-8y) which equals to becomes (-72xy). Now, multiply the (8y) with the (9x) which equal to becomes (72xy). Lastly (8y) multiplies with (-8y) equalling to (-64y²)

Overall the standard form would look like this:

81x² - 64y²

## How To Graph Factored Form

Or click on the embedded link below.

## Standard Form

## How to Factor Complex Trinomials #1

Or click on the embedded link below.

## How to Factor Complex Trinomials #2

This is another one of my videos that i made for Factoring Complex Trinomials

https://www.educreations.com/lesson/view/how-to-factor-complex-trinomials/27575797/?ref=link&s=aAHitkOr click on the embedded link below.

## Factoring By Grouping

This is my own video on how to factor with grouping.

https://www.educreations.com/lesson/view/grouping-final/27576038/?s=EqkFMm&ref=appemailOr click on the embedded link below.

## How To Use The Quadratic Formula

## Discriminant

## Common Factoring

Example 1: 2x² + 8

Common factor between 2x² + 8x is:

2x² - (2) (x) (x)

8x - (2) (4) (x)

The common factors in this equation is: (2) (x)

So you put the 2x in front and then put a bracket and then divide 2x² with 2x... and 2 is left and then you divide 8x with 2.....and 4 is left

This is how the answer will look like:

2x(x+4)

This is common Factoring

## Completing The Square

This is my own video on completing the squares

https://www.educreations.com/lesson/view/completing-the-square/27617938/?ref=link&s=MwtnC0

Or click on the embedded link below.

## How To Graph Vertex Form

Or click on the embedded link below.

## Word Problems

## Connections

**The connection between quadratics 1 is the graphing it was similarly used to the part 2 of the quadratics factoring. They were similar because once you factored them you were able to get the x-intercepts, then find the AOS and then sub in the x value to find the y value and after doing this from the factoring you were able to graph it by putting the x intercepts as points and then use the AOS and the y-value making the vertex, to make the parabola. Quadratics 2 related to quadratics 3 because in quadratics 2 you would factor and once you factored you would get 2 of the x-intercepts. The same way in Quadratics 3 we used Quadratic Formula to find 2 of the x-intercepts and once x-intercepts were found we can basically isolate for the y to get the y-value to find the vertex. Altogether the quadratics unit were summed up in different forms like Standard, Vertex and Factored form.**

**They all used the graphing method by find the x-intercepts to find the vertex. The Standard form looked like: y=ax² + bx + c. You could use standard form to answer word problems like to find the maximum height or when the ball will hit the ground it etc. It is also used to for Quadratic Formula when as the middle value is b and the last value is c and the first value is a. Secondly Factored form looks like: y=a(x-r) (x-s). This formula is used for factoring all types like Simple and complex trinomials and etc. Lastly, Vertex form looks like: y=a(x-h)² + k. This formula is used for perfect squares and many more. But mostly these forms relate to the graphing because these forms are just showing different ways you can do to graph. Like Factored form finds two x-intercepts to graph and so does quadratic formula these forms relate to our understanding to make life easier. So whenever there is a hard question we use the easiest way to answer the question instead of the long way. For example, Quadratic Formula and Factored Form both solving for x. Depending on the form and the question you use either one applicable.**

## Reflection

**In my opinion at the beginning of the unit i didn't like quadratics but as i started learn the different forms and factoring and using quadratic formula to find x-intercepts. I started to like Quadratics. In quadratics the most favourite part was factoring. Especially factoring by grouping. I scored really well on my test for the Factoring. The part I had a little struggle on was the word problems but as i started to put more effort on them at home . I started to understand how to do these word problems. As a also startedto have a better understanding on word problems in Optimization i liked the revenue questions. Overall, I think i did excellent throughout this unit.**