Quadratic Relationships!!

By: Jhanvi Shah

What does Quadratics have to do with real life?

Ever seen a person shoot a basketball? Have you closely seen how the ball goes into a net?

When the ball is going towards the net... it forms a curve! Now if we were to graph the flight of the ball, how would we do it? In Grade 9, we were taught about linear relationships in which the result of an equation (in the form of y=mx+b) would form a straight line if we were to graph it, but that doesn't help explain how to graph the flight of a basketball going into a net.... that's why we need quadratics!! Quadratics help show display the path of an object (or other things such as a dive) by using curves! Please look below for the Table of Contents and for everything that will be shown on this website!! I hope this website helps you learn about quadratics and answers all your questions... There are also some links posted for extra help and there are also videos. Feel free to leave comments/suggestions on the email provided for me to improve on. Thank you!!

Jhanvi :)


Introduction to Quadratics:

- Key features of Quadratic relations

- introduction to parabolas

- three ways to represent a Quadratic relation

Types Of Equations:

-Vertex form

-Factored form

-Standard form

Vertex form:

- Axis of Symmetry (x=h)

- Optimal Value (y=k)

- Transformations

- x-intercepts/ zeroes

- Graphing using vertex form

- ^ ties in with step pattern

Factored Form:

- Zeroes or x-intercepts ( r and s)

- Axis of symmetry ( x = r+s/2)

- Optimal value (sub in)

- Graphing using Factored form

Standard Form:

- Zeroes ( Quadratic Formula)

- Axis of Symmetry

- Optimal Value (sub in)

- Graphing using Standard form

- The Quadratic Formula

- The Discriminant

- Standard to Vertex

Factoring to turn into factored form:

- Multiply polynomials and binomials

- Common Factoring

- Special Products

- Simple Trinomials

- Complex Trinomials


- Solving equations using factored form

- Completing the square (part 1)

- Completing the square (part 2)

- Word problems


My Reflection

Key Features of Quadratic Relations

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In grade 9 we learned how to graph a linear relationship in which their would be a straight line made in a graph. In grade 10, we learn about quadratic relationships in which a curve would be made on a graph. Another word for that curve is a parabola. There are many different parts of a parabola:

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- Parabolas can open up or down

- 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 (AOS) divides the parabola into two equal halves

- The vertex of a parabola is the point where the AOS and the parabola meet.

- the vertex 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

- the vertex is a y-co-ordinate which is optimal value

Three ways to represent a Quadratic Relation

Types of Equations

The Vertex form

As you can see above, these are the three different Quadratic equations. Each equation has different parts and different ways to graph it. Please watch the video below that i have created explaining the different parts of the equation, how to graph it, and the step pattern:
Learn all about Vertex form

The Factored Form

The video above showed you the different parts of the vertex form equation, how to graph it and also how to use the step pattern. A Factored form equation is very different from a vertex form equation because the meaning of the parts is different and how to graph it, is also very different. Please watch another video that i have created to learn about the different parts, and how to graph using the Factored Form:
All about the Factored form

Standard Form and Quadratic Formula

Well now you know about Vertex form and Factored form, there's one more form your gonna need to know about and that is Standard form!! It ties in with factored form and is a pretty easy form to learn about. You will also learn about the Quadratic formula and also how to convert a standard form equation into a factored equation. Please watch the video below:

The Discriminant

The discriminant is not a new lesson, it actually ties in with the Quadratic formula. Please watch the video below:
The Discriminant

We will also be learning different types of factoring

Multiplying polynomials and binomials

Before we learn about the different types of factoring.. why don't we do a quick lesson on factoring so it will help you out with the different types of factoring. Please watch the video below:

Common Factoring

Remember learning about the GCF (greatest common factor) in grade 9? Well guess what... that's all you need to know for common factoring!

Common Factoring is when in an equation, there is a number or variable that you can divide out evenly. Its basically finding the Greatest common factor and factoring it out of the equation, but that doesn't mean you get rid of it! That number is placed in front of the brackets. Please watch the video below to see an example:

Common Factoring

Simple Trinomials

Now that we've learned about expanding and factoring, i think we should move onto simple trinomials. Please watch the video below for further explanation and an example:
Simple Trinomials

Complex Trinomials

Simple trinomials wasn't that hard was it? Now that you know all about simple trinomials, i think its time to take our understanding to a new level. Remember that the standard form equation is Y=ax^2+bx+c and in simple trinomials "a" was always 1 but now i will be teaching you about complex trinomials in which "a" can be any number. Please watch the video below:
Complex Trinomials

Special Products

Now that you know about all the other types of factoring... lets learn something easy. Special products are divided into two parts: Perfect Squares and Difference of Squares. Please watch the video below:
Special Products


There's so much to know about factoring that im pretty sure some of what we learned must be forgotten. But no worries! Thanks to the amazing Mr.Anusic... we have a video review all the different types of factoring. Please watch the video below for review:
3.11 Factoring

Heres something that will help!

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Solve Equations using Factored Form

Please watch the video below:
Solve equations in Factored Form

Completing the Square (part 1)

Learn about the ancient method of converting quadratics from standard to vertex form so they can be solved. Please watch the video below:
Completing the Square (part 1)

Completing the square (part 2 and review for part 1)

there's no better way to learn than learning from others and that indeed what im doing now. Here's another video from Mr.Anusic explaining about completing the square and there's also a link that will further more explain about completing the square:
3.14 Completing the square

Word Problems

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Optimization word problems

Here is some types of word problems that we took up in class.. these are optimization word problems so its mostly about finding the min/max point.
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Heres a video from Mr. Anusic... talking a little about motion problems which are another type of word problems you should know:
3.12 Motion problems

At the end... arent they all connected?

To think about it everything you learned falls in together. Everything we learned falls into the different types of forms or how to convert them from one form to another. Simple trinomials and complex trinomials are basically the same because at the end the only difference between them is the number in front of "a". When we were taught this unit, we divided it up into quadratics: 1, 2 and 3. First we learned about what quadratics was, parabolas, and the different forms. Then we learned how to factor them and change them from one form to other. And finally we learned about solving for different parts of the parabola. This all leads to the final product which may be the equation or the parabola but at the end its all tied into one big unit..... QUADRATICS!! They're all going back to the different forms and are all tied in to show a quadratic relation.
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My Reflection

Well As you can see, that was a picture of my Quadratic part 1 Mini test. i did pretty good in knowledge and application but my communication part was done poorly. So i also posted a picture of my Quadratics 2 mini test communication part, in which i got a 3+ which was not that bad. I understood the concept of the different forms and how to graph them, that i believe is my strongest point in quadratics, i also am very good at simple trinomials, using the quadratic formula, and finding the vertex or zeroes of a graph. My weak points would be that i get confused at first when i see an equation, because im not sure which type of factoring to do which slows me down, i also need to work on word problems. I found quadratics easy because it divided which helped me concentrated on different areas. i also found the quadratic formula a short and simple way to help me out. Overall, i think i did pretty good in this unit and i hope to improve my weak areas.
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Useful links

Thank you for visiting my website!! I hope you learned everything about Quadratics that you need to know!! Come Again Soon!!! :)