Welcome to the World of Quadratics

By: Aarani Kirubaharan


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


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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."
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Here is everything you need to know about parabolas...

  • 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

Types of Equations

Vertex Form

Vertex form is one of the three Quadratic equations, as shown above. Each form is a different way to graph it. Please watch the video in order to see all steps of vertex form, how to graph it and about the step pattern.
Beginning to vertex form
Example for vertex form

Factor Form

Followed by the Vertex form video, the second equation is factor form. Factor form is different from vertex form because the meanings to each part is now different.
Factored form

Standard Form

The last form you need to learn is Standard form. It is similar to Factored Form but you need to figure out the zeros/x-intercepts on your own instead. You also need to know the Quadratic Formula, which is also provided in the video. Please watch the video below the text.
Standard form


The discriminant is an addition to the previous video which ties in with Quadratic Formula. Please watch the following video
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Types of Expanding


Before we start let's learn a little about factoring so it will help you out with the different types of factoring.

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

Simple trinomials

Moving onto Simple trinomials now... Please watch the video up next to learn about them.
Factoring simple trinomials

Complex Trinomials

Complex trinomials aren't much different from simple trinomials, but there are some differences. Please watch the video below to learn more about them.
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

Now that you've learnt all about factoring, I'm going to show you how to solve equations from Factored Form. Please watch the following video to get a better understanding.
Solving equations in factored form

Completing the Square

Completing the square is a method used to convert Standard Form to Vertex form. Vertex Form is better to use because we can figure out the plot points, vertex and solve. Please watch the video to understand better.
Intro to completing squares
Completing the square

Word Problems

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Mini Test

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