# Welcome to the World of Quadratics

### By: Aarani Kirubaharan

## HOW CAN QUADRATICS RELATE TO REAL LIFE

Have you ever noticed the curved pattern in something such as the example in the picture? have you noticed the path of the Fireball before it hits the ground. How would that look like if we were to graph it?

As known, in Grade 9, we learnt about linear relationships in which we would graph a line that would be straight. The equation to that would be the y = mx+b form. Now looking at the Fireball picture, how would you now graph a curved relation? Well that's where Quadratics comes in... In this website you will find various topics explaining the components of Quadratics.

## Table of Contents:

**Introduction to Quadratics**

- Key terminology of quadratic relations
- Introduction to Parabolas
- Ways to express the Quadratic relations

**Types of equations**

- Vertex form
- Factored form
- Standard form

**Vertex Form:**

- Axis of symmetry (x=h)
- Optimal Value (y=k)
- Transformations
- Graphing using vertex form
- How step pattern relates Vertex form

**Standard form:**

- Quadratic formula (zeros)
- Discriminant

**Types of Factoring:**

- Expanding
- Common Factoring
- Simple trinomials
- Complex trinomials
- Special products: Perfect squares & Difference of squares

**How to solve equations in Factored Form**

- Finding the zeros/x-intercepts
- Standard Form to Factored Form for solving
- Solving from Fractions

**Completing Squares**

- Finding the "C value"
- Converting Standard Form to Vertex Form

## KEY TERMINOLOGY OF QUADRATIC RELATIONS

## Parabolas

In Grade 9, we learnt about linear relationships and how to graph them, whereas in Grade 10 we learn about quadratic relationships in which a curve would be made on a graph. The "curve" in any relationship is also known as the "Parabola."

- Parabolas can open up down (Positivity increase or Negativity decrease)
- The Zero of a Parabola is where the graph crosses the x-axis
- "Zeroes" can also be called "x-intercepts" or "roots"
- The Axis of symmetry divides the Parabola into 2 equal halves
- The vertex of a Parabola is the point where the axis of symmetry and the Parabola meet. It is the point where the Parabola is at its maximum or minimum value
- The optimal value is the value of the "y" co-ordinate of the vertex
- The y-intercept of a Parabola is where the graph crosses the y-axis

## Ways to Express Quadratic Relationships

## Equations You can tell if an equation is Quadratic when you see the exponents "2". | ## Table of values In a linear relations, the 1st difference would be the same. But, if the 2nd differences are similar then it is a Quadratic Relationship. If there is no similarities then there is no relationship present. | ## Graphing The last way to represent a quadratic relation is by making a parabola. (Graphing it) |

## Table of values

In a linear relations, the 1st difference would be the same. But, if the 2nd differences are similar then it is a Quadratic Relationship. If there is no similarities then there is no relationship present.

## Types of Equations

Beginning to vertex form

Example for vertex form

Factored form

Standard form

Discriminant

## Types of Expanding

Expanding

## Common Factoring

In grade 9 we learnt about the greatest common factor (GCF). Common Factoring is when in an equation, there is a number or variable that you can divide out evenly. One thing we need to remember about common factoring is that just because you divide a number or variable out doesn't mean it disappears. The number or variable in front/outside of the brackets. Please watch the following video to get a better understanding.

Common factoring

Factoring simple trinomials

Complex trinimials

## Special Products

Special products are divided into two parts: Perfect Squares and Difference of Squares. Special products are very simple to learn and remember. Please watch the following video for more informations

Special products: perfect squares and difference of squares

## How to solve equations in Factored Form

Solving equations in factored form

## Completing the Square

Intro to completing squares

Completing the square