QUADRATIC RELATIONSHIPS

EVERTHING YOU NEED TO KNOW ABOUT GRADE 10 QUADRATIC!!!!!!!

BY: JASDEEP PALHA

Overview of Flyer

Everywhere we go, we are interactive or exposed to quadratics and parabolas.To get this type of relation you must have the same second differences. Unlike linear relations where the first difference is equal. The second differences make the curve or in mathematical terms called a parabola.

In quadiratics we will learn

  1. important term a definitions
  2. second differences/ first differences
  3. types of equations
  4. factoring
  5. graphing
  6. converting
  7. solving
  8. word problems
  9. test reflection
  10. connection table
  11. more videos and links
  12. assesments

Terms & Defintions

  • X-intercept- where the parabola intercepts with the x-axis
  • Y-intercepts- where the parabola intercepts with the y-axis
  • Zeros- the x value which makes the equation equal to zero
  • Axis of symmetry- the vertical line which cut the parabola down in the middle
  • Optimal value- the tip of the parabola the lowest or highest point of the parabola
  • Vertex the maximum or minimum point on the graph changes direction
  • These terms are very important to know since they will be refered to in this unit and within in the flyer

Forms of Equations

There are 3 forms that quadratic equations can be written in.
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Standard form

To graph a standard form equation you must convert it. Look in the converting section for more information on this. The standard form equation is written as y= ax^2+ bx+ c.

Vertex Form

Vertex form is one the most efficient ways a equation can be written so that it is easily graphed. The form of it is y= (X- h)^2+x. Below the diagram show the different parts of a vertex form equation. The vertex is the h and the x variable. The x value is the h and y value is x. If any part of the vertex is in a bracket it will be the opposite sign. In this case -h wont be -h but +h.
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  • Vertical reflection- if the sign is negative the parabola will open down if it is positive the parabola will open up
  • vertical stretch/ compression- if the number is higher than on it is a stretch if it is less than one it is a compression
  • horizontal translation- the x value in the vertex whether it is negative or positive it is still translation
  • vertical translation- opposite of horizontal translation, y value of vertex

Factored Form

Factored form is another easy way graphing could be done. In this form the x- ints/ zeros are given and we have to find the vertex. The form it is written in is y= a(x-x1)(x-x2). Instruction on how to find vertex graph etc..., can be found in the graphing video in the graphing portion.

First & Second Differences

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The chart above is the process to find out if your data is a parabola without graphing. You must know how to find first differences(fd). To start off you must label the numbers as y1, y2, y3 ... As I have done. In my data the number 0 is y1 and 3 is y2. To get 3 as my fd I have subtracted y1 from y2. 0 subtracted from 3 is 3. This is the process of finding fd you just continue, so for the next fd you have to do y4-y3. What is new is ,second difference. The process must be used to find second differences( sd) except we have to subtract the fd. So basically label the fd as y1, .... And subtract y1 from y2 ect. Now that you learned how to find fd ans sd try to fill in the chart below on a paper for practice.
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Factoring ( simple )

Factoring simple trinomials is a very simple process as the process is called "simple" trinomials. To start off for any type of factoring you must know expanding and simplifying. Below is a example of expanding and simplifying and factoring a simple trinomial.
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Since we have a bracket we must expand it first according to BEDMAS

Once the bucket is expanded you must collect like terms to simplify the equation

At this point your equation should be full expanded and simplified.

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A simple trinomial is written in x squared + ax+ b. x squared can be square rooted and become ( x) (x) into two different brackets. As shown in the above diagram the la two number ax and b have something in common which is two numbers that are multiplied = b and the same numbers multiplied = ax. In the case above ax= 5x and b= 6. So the start off start siting the factors of six. Look below.
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Now we just plug in the two numbers into the blanks from the original equation.
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One last step is to check that your answer is right. You will do this be expanding and simplifying the factored equation. Look below.
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Factoring ( common)

Common factoring is similar to similar factoring. When the equation has all parts that have a common factor this is the write formula to us. An example that you should us common factoring in is the equation below
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Now I will be showing you how to factor this equation using common factoring methods.
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Now you just simple factor.
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Factoring ( Complex)

Now thing will be getting a little more complicated so be sure to understand all above aspects so you can understand the next part you have to learn.

So complex trinomials are written in a similar form to common trionomial put don't have any common numbers. There we are not able to factor it using common factoring methods. Below you can look at the way you can factor a complex trinomial. Also read the description ahead to farther understand this form of factoring.

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Now you will need to use some of the factoring methods listed above.
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Factoring ( Differ of Squares)

Factoring in difference of squares is used when 2 squares are subtracted.
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Factoring ( perfect square)

This is one the most hardest form of facting so make. Sure you oay full attention!
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Graphing

Graphing vertex form, standard form and factored form will be demonstrated in the video below . For vertex form it will also include the step pattern.
Graphing vertex form
Quick Way of Graphing a Quadratic Function in Vertex Form
Graphing a parabola in vertex form
Graphing factored form
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Graphing standard form
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Converting

May times people experience difficult in converting certain forms into a different form. This part will basically put the whole unit together for you. Please pay detailed attention to the next bit of information. To start of with there are three ways we can convert our different forms , factoring , completing the square and by using the quadratic formula.



Factoring- is used when values are easily factor able, for example x^2+2x+3 (follow steps above in Factoring)


Completing square- Is used when values are factor able, but hard to think of mentally. Look below for the correct way of performing this function.


Quadratic formula- is used when equation is complex or hard to factor, This equation consist of x=-b+- (square root of b^2-4ac)/ 2a. this gives us the two zeros, x intercepts or roots. Look below for the correct way of performing this function. ( DISCRIMINANT WILL BE INCLUDED)

completing the square: is used to change standard form to vertex form.

work is still to be added.

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While using the quadratic formula before square rooting the final number in the square root is called the discriminant. When you have the discriminant you know if you formula is going to have a possible answer if the number is not negative. If the number is negative we know that there is no square root for that so the answer will be not possible. You can also calculate the discriminant by a formula that is called the discriminant which is b^2-4ac.

Solving

When you have an equation and you must find the the variable value use the solving method. below are steps and examples of solving equations.
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Word Problems

In the unit of quadratics there are many times you will come across word problems. For help in solving word problems look at the variety of word problems below.

Word problems can be tuff, but if you follow the steps and read the problem correctly.


Step 1-

Read the problem and write down given information


Step 2-

Try to think of an equation that can solve the problem


Step 3-

Use factoring, graphing, converting, solving to solve the problem.

examples of word problems

1. Jasdeep is selling T- shirts. his regular price is 20 dollars and he usually sells 15 t- shirts a day. Mandeep finds that for each reduction in price of 1 dollar he can sell to more t- shirts

a) create an algebraic model to represent Jasdeep total sales revenue.

b) determine the maximum revenue and the price at which this maximum revenue will occur.


( THE ANSWER TO THE WORD PROBLEM WILL BE SHOWN BELOW, SOAK IN THE WAY OF SOLVING IT IN)

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2. The garden is enclosed on three sides using 60m of fencing. the remaining side is formed by the wall of a garage. draw a diagram. What dimensions enclose 450m^2 of garden?


( THE ANSWER TO THE WORD PROBLEM WILL BE SHOWN BELOW, SOAK IN THE WAY OF SOLVING IT IN)

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3. a right angle triangle has a hypotenuse 2x+1, and the two other sides are x and x+4. determine the value of x, and then the length of each side.

( THE ANSWER TO THE WORD PROBLEM WILL BE SHOWN BELOW, SOAK IN THE WAY OF SOLVING IT IN)

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Comments on Tests

Below are some test i did and a brief explanation why I performed weak or why i did good please take a look so you don't make the same mistakes. Also try some questions out for practice.

THE QUESTION BELOW IS A QUESTION FROM VERTEX FORM PARABOLAS, AND IT WAS ASKING TO EXPLAIN THE TRANSFORMATION.( THIS IS QUESTION NUMBER 9).

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The reason i got perfect on this question was because i explained every single part of the transformation. The equation was written in vertex form which meant the vertical reflection, horizontal translation, vertical translation and vertical stretch is shown. In this case there was a vertical reflection since the a value was a negative( -2 ). The horizontal translation was 3 units right sine the x value of the vertex is 3 and 3 is to the right of the center line in a graph. The vertical translation was 5 units up since the y value of the vertex is +5. this was a vertical stretch due to the number in front of the bracket (a) being a number higher than 1 which meant there was a change in the step pattern.
Below is a question on our first quiz for quadratics.
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In the question above question number 3 my calculations were right but the sign was wrong which ca cause your answer to wrong. Always remember not to get mixed up and check your work twice for small mistakes like mine due to carelessness.

Additional Information

WATCH THE VIDEOS BELOW FOR MORE EXPLANATIONS AND BETTER WAYS OF REMEBERING FORMULAS
Quadratic Inequalities
❤² How to Solve Quadratic Equations By Factoring (mathbff)
❤² How to Solve By Completing the Square (mathbff)
THE VIDEO BELOW MAY INCOURAGE YOU!!!!!!!!
You're Not Bad At Math, You're Just Lazy
Algebra - Quadratic Functions (Parabolas)
Algebra - Quadratic Formula
Algebra - Completing the square
Solve Quadratic Equations using Quadratic Formula
Quadratic Formula Cup Song
The "One Direction" Quadratic Formula Song
Quadratic Formula Song to Adele's "Rolling In The Deep"
Quadratic Formula Song Rockford Christian
Quadratic Formula - the Musical
Quadratic Formula Pop Goes the Weasel
The Quadratic Equation Song
Do The Quad Solve (WSHS Math Rap Song)
Graph! (WSHS Math Rap Song)

My Reflection

Over all, quadratics is very simple to understand. Their are many ways to understand these problems, including factoring, converting, graphing and solving. if you follow the steps correctly and read the question carefully, guaranteed you will become a pro in understanding quadratic relations. at last I hope you found my flyer helpful, and I hope you have now become a pro in understanding quadratic equations.

Connections Chart

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Assesment

After you are done cursing this flyer you should be ready to asses yourself, visit the link below.

http://ca.ixl.com/math/grade-10

My Message

Now that you have went through this website i would like to say thank you. this unit could be a disaster if you don't follow trough so always pay attention. good luck learning. Once again THANKS.