Welcome to the World of Quadratics
By: Aarani Kirubaharan
HOW CAN QUADRATICS RELATE TO REAL LIFE
As known, in Grade 9, we learnt about linear relationships in which we would graph a line that would be straight. The equation to that would be the y = mx+b form. Now looking at the Fireball picture, how would you now graph a curved relation? Well that's where Quadratics comes in... In this website you will find various topics explaining the components of Quadratics.
Table of Contents:
- Key terminology of quadratic relations
- Introduction to Parabolas
- Ways to express the Quadratic relations
Types of equations
- Vertex form
- Factored form
- Standard form
- Axis of symmetry (x=h)
- Optimal Value (y=k)
- Graphing using vertex form
- How step pattern relates Vertex form
- Quadratic formula (zeros)
Types of Factoring:
- Common Factoring
- Simple trinomials
- Complex trinomials
- Special products: Perfect squares & Difference of squares
How to solve equations in Factored Form
- Finding the zeros/x-intercepts
- Standard Form to Factored Form for solving
- Solving from Fractions
- Finding the "C value"
- Converting Standard Form to Vertex Form
KEY TERMINOLOGY OF QUADRATIC RELATIONS
- Parabolas can open up down (Positivity increase or Negativity decrease)
- The Zero of a Parabola is where the graph crosses the x-axis
- "Zeroes" can also be called "x-intercepts" or "roots"
- The Axis of symmetry divides the Parabola into 2 equal halves
- The vertex of a Parabola is the point where the axis of symmetry and the Parabola meet. It is the point where the Parabola is at its maximum or minimum value
- The optimal value is the value of the "y" co-ordinate of the vertex
- The y-intercept of a Parabola is where the graph crosses the y-axis
Ways to Express Quadratic Relationships
You can tell if an equation is Quadratic when you see the exponents "2".
Table of values
In a linear relations, the 1st difference would be the same. But, if the 2nd differences are similar then it is a Quadratic Relationship. If there is no similarities then there is no relationship present.
The last way to represent a quadratic relation is by making a parabola. (Graphing it)