Quadratic Relationships
By: Harman Virk
LEARNING GOALS
First/Second Differences
Linear
If the first differences are the same (in this case all the differences are 6) it means that it's linear.
Quadratic
All of the second differences are the same and this is an example of quadratics.
Neither
This is neither linear or quadratic.
Transformations
Determining an equation using 2 points
Learning Goal 3
SUMMARY OF THE UNIT
The Step Pattern
How the step pattern works
The odd numbers (1,3,5) are multiplied by the "a" value. In the first example the numbers are multiplied by 1, in the second example the numbers are multiplied by 2 because that is the value of "a".
GRAPH
a>1 or a<-1
Vertically stretched by a factor of 2
-1<a<1
Vertically compressed by a factor 0.5
a<0
Reflected in the x-axis
WORD PROBLEM USING VERTEX FORM
The flight path of a firework is modeled by the relation h=-5(t-5)2+127 where h is the height, in metres, of the firework above the ground and t is the time, in seconds, since the firework was fired.
a) What is the maximum height reached by the firework?
The maximum height is 127 m.
b) How many seconds after it was fired does the firework reach this height?
The firework reaches 127 m after 5 seconds.
VIDEO
Video Using Transformations