By: Hashim Mohamed
Table of Contents
Intro to Parabolas
First and Second Differences
Vertex Form: y=a(x-h)^2 +k
-Axis of Symmetry
-X-int or zeroes
-Finding an equation for a parabola
Factored Form: y=a(x-r) (x-s)
- X-int or zeroes
- Axis of symmetry
- Optimal value
Standard Form: y=ax^2+bx+c
-axis of symmetry
- Using completing the sq to turn into vertex
- Difference of squares
Here are some important terms to remember, this is what makes up a parabola.
Axis of Symmetry: It's in the middle of your parabola. It helps to find your vertex.
Vertex Point: This is the curve of the parabola. It's the direction of where it faces.
Optimal Value: This is the value of your vertex.
FIRST AND SECOND DIFFERENCES
Below is a chart of an example of the first and second differences.
Vertex form: h= a(x-h)2 +k
Factored form: a(x-r) (x-s)
Standard form: ax2+bx+c=0
Ex. y= -2(x-2)^2 +3
Vertical Reflection: If it's a - the parabola will open downwards. If it's positive it will open upwards.
Vertical Stretch: This effects the step pattern instead of doing the basic step pattern routine it will double instead look below.
Horizontal Translation: This moves the parabola left or right. It's also the part of the vertex.
Vertical Translation: This moves the parabola up or down. It's also a part of the vertex.
GRAPHING VERTEX FORM
FINDING AN EQUATION FOR A PARABOLA
COMMON FACTORING AND EXPANDING/SIMPLIFYING
SIMPLE TRINOMIAL FACTORING
You can use trial and error which is a method known for finding the terms by taking a guess and seeing if its correct. We'll use that in complex factoring as well.
COMPLEX TRINOMIAL FACTORING
PERFECT OF SQUARES & DIFFERENCE OF SQUARES
Perfect Squares must follow the formula of (a+b) (a+b).
Difference of squares must follow the formula of (a-b) (a+b).
To see if its a difference of squares you must check for:
1. If the term is a square
2. If there is a - in between the two numbers.
COMPLETING THE SQUARE AND TURNING IT INTO VERTEX FORM
The formula is below with an example.