# Quadratic Relationships

### By: Banvir Ghumman

## What Even is a Quadratic Relationship?

## Graphing Using Vertex Form

## Summary of the Vertex Form

- 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

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.

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

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

## Word Problem using Vertex Form

## Graphing Transformations

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.

## Common Factors/ GCF

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.

## Expanding Factored form/ Multiplying Binominals

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

## R and S value

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

## Graphing Factored Form

## Simple Factoring/Factoring X2+ bx+c

## Solving Word Problems using factoring

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

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

## Maxima and Minima

## Solving Quadratic Relations

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

## Word Problems using Quadratic Formula

## Personal Video

## My best assessment mark

## Learning Goals

Learn how to use quadratic formula

Learn how to complete a square