By: Jhanvi Shah
What does Quadratics have to do with real life?
Ever seen a person shoot a basketball? Have you closely seen how the ball goes into a net?
When the ball is going towards the net... it forms a curve! Now if we were to graph the flight of the ball, how would we do it? In Grade 9, we were taught about linear relationships in which the result of an equation (in the form of y=mx+b) would form a straight line if we were to graph it, but that doesn't help explain how to graph the flight of a basketball going into a net.... that's why we need quadratics!! Quadratics help show display the path of an object (or other things such as a dive) by using curves! Please look below for the Table of Contents and for everything that will be shown on this website!! I hope this website helps you learn about quadratics and answers all your questions... There are also some links posted for extra help and there are also videos. Feel free to leave comments/suggestions on the email provided for me to improve on. Thank you!!
TABLE OF CONTENTS:
Introduction to Quadratics:
- Key features of Quadratic relations
- introduction to parabolas
- three ways to represent a Quadratic relation
Types Of Equations:
- Axis of Symmetry (x=h)
- Optimal Value (y=k)
- x-intercepts/ zeroes
- Graphing using vertex form
- ^ ties in with step pattern
- Zeroes or x-intercepts ( r and s)
- Axis of symmetry ( x = r+s/2)
- Optimal value (sub in)
- Graphing using Factored form
- Zeroes ( Quadratic Formula)
- Axis of Symmetry
- Optimal Value (sub in)
- Graphing using Standard form
- The Quadratic Formula
- The Discriminant
- Standard to Vertex
Factoring to turn into factored form:
- Multiply polynomials and binomials
- Common Factoring
- Special Products
- Simple Trinomials
- Complex Trinomials
- Solving equations using factored form
- Completing the square (part 1)
- Completing the square (part 2)
- Word problems
Key Features of Quadratic Relations
In grade 9 we learned how to graph a linear relationship in which their would be a straight line made in a graph. In grade 10, we learn about quadratic relationships in which a curve would be made on a graph. Another word for that curve is a parabola. There are many different parts of a parabola:
- Parabolas can open up or down
- 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 (AOS) divides the parabola into two equal halves
- The vertex of a parabola is the point where the AOS and the parabola meet.
- the vertex 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
- the vertex is a y-co-ordinate which is optimal value
Three ways to represent a Quadratic Relation
Table of Values
In a linear relation, the first differences have to be the same but in a Quadratic relation, the second differences have to be the same
This is another way of representing a quadratic relation, by graphing it (making a parabola)
Exponent of "2"
When there is the exponent "2", you know automatically that it is an Quadratic equation (relation)
Table of Values
Types of Equations
The Factored Form
Standard Form and Quadratic Formula
We will also be learning different types of factoring
Multiplying polynomials and binomials
Remember learning about the GCF (greatest common factor) in grade 9? Well guess what... that's all you need to know for common factoring!
Common Factoring is when in an equation, there is a number or variable that you can divide out evenly. Its basically finding the Greatest common factor and factoring it out of the equation, but that doesn't mean you get rid of it! That number is placed in front of the brackets. Please watch the video below to see an example: