Quadratic Relationships

By: Banvir Ghumman

What Even is a Quadratic Relationship?

A Quadratic relationship is used to define the involvement of relations of an unknown quantity and variables

Graphing Using Vertex Form

Summary of the Vertex Form

The vertex form is a equaation that helps you figure out the vertex of a graph.


  • Helps with finding out if the parabola is stretched or compressed parabola is (a)
  • Tells you the vertex (h,k)
  • Helps you figure out if the vertex opens up or down
  • To find y-intercept set x=0
  • To solve x-intercept set y=0 and solve to get the standard equation and simplify with the quadratic formula
What does the H value in a vertex Mean?


This value is to help figure out the x value and also H defines the transformation if it is negative the vertex moves left and if it is positive the vertex will move right.

What does the K value in a vertex mean?


This value is to help figure out the y value and also k defines the transformation of if k is positive the vertex will move up and if k is negative the vertex will move down

What is the value A In the vertex form


The parabola is the A value that transforms the vertex by stretching the parabola on the x value

A= Positive opens up

A= Negative opens down

First and Second Differences

To start of first you need to know about 1st and 2nd differences. To figure out first differences you need to subtract or add your y values to see the difference and if the difference is the same so if your two y values are 1 and 2 the difference is 1 throughout the y column this makes it linear because it does not change. For second differences if the y values do not have the same difference you then do the same but this time with your 1st differences instead if they match they are then linear if not they are called neither.
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Word Problem using Vertex Form

writing an equation in vertex form- word problem

Graphing Transformations

Graphing Quadratic Transformations (Grade 10 academic Lesson 4.4).mov
Learning Goals


Learn how to graph vertex form

Learn the difference between 1st and 2nd differences

Learn how to use the vertex equation

Sources

Khan Academy. N.p., n.d. Web. 08 May 2016.


Grundlehren Der Mathematischen Wissenschaften Modular Units (1981): 58-80.Page 6 for the Image. Web.

Part #2 Factored Form

What is Factored Form?

form of an algebraic expression in which no part of the expression can be made simpler by pulling out a common factor.

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Common Factors/ GCF

To make using factored form easier you need to know what common factors are this is the highest number that divides into two or more numbers.


The factors of a number are two numbers multiplied together to equal that number an example would be if you have 15 and 24 they have a common factor of 3 because 15 can be multiplied 3x5 and 24 can be multiplied 3x8


Also GCF which is the greatest common factor which is found when solving for common factors the greatest common factor is highest number that can be multiplied to get the number as shown in the picture below.

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3.7 Common Factoring

Expanding Factored form/ Multiplying Binominals

When expanding factored form you need to multiply the numbers within each other to get your equation so if you have (x+1)(x+2) you need to multiply (x+1) both numbers with (x+2)

so you would end with x(squared) + x2 + 1x+ 3 as your standard form

R and S value

R and S values are the x-intercepts in this case R1 is equal to= R and R2 is equal to =S

R and S are values that initially will end up always being your x intercepts

Also A will always be equal to 1

A=1

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Graphing Factored Form

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Simple Factoring/Factoring X2+ bx+c

Example 4: Factor a polynomial with two variables by taking a common factor | Khan Academy
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Solving Word Problems using factoring

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8-5 Example 3 A Word Problem using Factoring
Learning Goals


To learn how to multiply polynomials

To learn how to factor using a graph

To Learn how to solve a word problem using factoring

Sources

YouTube. N.p., n.d. Web. 08 May 2016.


YouTube. YouTube, 17 Jan. 2014. Web. 08 May 2016.

Part # 3 Standard Form

Summary of this unit


In this unit you learn about many different things which are maxima and minima, completing the square, solving quadratic equations and graphing quadratics using the x- intercepts

Completing the Square

To start of to make solving this equation easy you want to make sure your equation is in standard form by expanding your vertex equation. When solving this you want to first start of by moving the loose number to the opposite side. Now you factor out whatever number is with the squared term so if it is 3x squared you factor out 3 as in divide it not get rid of it. Then you move on with Create space on the left hand side and this is by taking half of the co-efficient from the inside in this problem it would be 3. Then you would want to convert the right hand side to squared and multiply out the a times. Next step would be to simplify then move the loose number back to the right side and reformat it into vertex form.
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Maxima and Minima

Identifying minima and maxima for x^3 - 12x - 5

Solving Quadratic Relations

Quadratic Formula
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To start of the first step would be to write the quadratic equation in standard form ax^2+bx+c=0.

Secondly you need to determine the values of abc from the question or word problem or etc.

Lastly substitute the values in the formula and simplify

Also the value of C is the y-intercept and the value of A is different shape or size of opening

Graphing Using X- Intercepts

6.3-Graph Quadratics Using X Intercepts

Word Problems using Quadratic Formula

Example 4: Applying the quadratic formula | Quadratic equations | Algebra I | Khan Academy

Personal Video

Completing the square to get the vertex form

My best assessment mark

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My best question from the quadratic standard form test although this is not my best work this is my best question I can do much better by continuing with doing my homework

Learning Goals

Learn how to graph quadratics using x-intercepts

Learn how to use quadratic formula

Learn how to complete a square