Quadratics Relationships
By : Anmol Saggu
What is Quadratics
Where are Parabola used in daily life
Table of Contents
1 Introduction
- Analyzing quadratics (second differences)
- Introduction to parabolas
-Transformation
2 Types of equations
- Vertex form
- Factored form
- Standard form
3 Factored form
- Common factoring
- Factoring simple trinomials
- Factoring complex trinomials
- Special cases
- Difference of squares
- Perfect square
- Factoring by grouping
- Graphing factored form
4 Vertex form
- To find an equation when only given the vertex
- Isolating for x
- Graphing vertex form
5 Standard form
- Completing the square (standard to vertex)
- Graphing from standard form
- Solving using quadratic equation
- Discriminant
Analyzing quadratics (second differences)
If none of them are same then it's neither
Introduction to Parabolas
A Parabola can either open upwards or downwards depending on the A value. If the A value is a positive number then the parabola will open upwards and if the A value is a negative number then the parabola will open downwards.
Main components of a parabola
Vertex - where the axis of symmetry and parabola meet
The axis of symmetry - divides the parabola into two equal halves
Optimal value - the y co-ordinate of the vertex/ highest or lowest point
X- intercepts - the zeroes
Y- intercept - when the graph crosses the y-axis/ y ≤ optimal value or y ≥ optimal value
vertex
X- intercepts/Zeros
optimal value
Axis of Symmetry
Formula of AOS : A+B/2
to find AOS -2+4/2 = 1
the AOS of this parabola is 1 as u can see in the picture
step pattern
Desmos!! It's a great app to check your parabola answers on your electronic device
quadratic Transformations
Vertical Translation: It is a type of translation in which the parabola can be moves right or left depending on the value of "H"
Vertical Stretch/Compression: vertical stretch is when the parabola stretches or expands. it is only possible if the "A" value is bigger than 1. Vertical compression is when the parabola gets thin and small. That happens when the "A" value is less than 1.
Vertical Reflection: A vertical reflection is when the parabola flips or reflects vertically
3 Different Types of Quadratic Forms
1.Vertex Form - y= a(x-h)^2+k
2.Standard Form - y=a(x-r) (x-s)
3.Factored Form - ax^2+bx+c