# QUADRATIC RELATIONSHIPS

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

## BY: JASDEEP PALHA

## Overview of Flyer

## In quadiratics we will learn

- important term a definitions
- second differences/ first differences
- types of equations
- factoring
- graphing
- converting
- solving
- word problems
- test reflection
- connection table
- more videos and links
- 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

## Standard form

## Vertex Form

- 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

## First & Second Differences

## Factoring ( simple )

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.

## Factoring ( common)

## Factoring ( Complex)

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.

## Factoring ( Differ of Squares)

## Factoring ( perfect square)

## Graphing

__Graphing vertex form__

__Graphing factored form__

__Graphing standard form__## Converting

**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.

## Solving

## Word Problems

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

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)

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

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

## Comments on Tests

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

## Additional Information

http://www.themathpage.com/alg/quadratic-equations.htm

http://onstudynotes.com/notes/mpm2d-grade-10-math-quadratics-relations-test/

http://ca.ixl.com/math/grade-10/solve-a-quadratic-equation-by-factoring

http://vlc.ucdsb.ca/content.php?pid=383897&sid=3146463

OR

GO TO THE BEST MATH GUYS YOUTUBE CHANNEL TO DO GOOD IN MATH FOR ANY TOPICS LINK IS BELOW!