1) Quadratic Functions
A quadratic function is an equation that contains x2 as the
highest power.
Examples are:
y = x2
y = x2 + 1
y = x2 + 3x - 1
y = -2x2 + 4x
y = x2 – 9
Example 1
Draw the graph of y = x2 + 1
NOTE: The special features of the parabola include:
The vertex
The concavity
Example 2
The area (A) of a rectangular garden of length x metres is given by A = 6x − x2.
a) Complete the following table of values:
b) Draw the graph of A = 6x − x2 using the table of ordered pairs.
c) What is the maximum area of the garden?
d) What is the maximum area of the garden?
Example 2 - Answers
a) Complete the following table of values:
Homework
Ex 12A p. 353 – 354 Q1 – 14
2) Cubic Functions
A cubic function is an equation that contains x3 as the highest
power.
Examples are:
y = x3
y = x3 + 1
y = x3 – x2 + 3x - 1
y = -2x3 + 4x
y = x3 – 9
Example 1
Draw the graph of y = x3
NOTE: The special features of the cubic include:
The point of inflexion
The gradient
3) Exponential Functions
An exponential function is an equation that contains x as the
exponent (power).
Examples are:
y = 2x
y = 2x + 1
y = 32x
y = - 2x
y = 3-x
Example 1
Draw the graph of y = 3x x y
-2
-1
0
1
2
Example 1
NOTE: The special features of the exponential include:
The exponential has a “tail” and it increases very quickly
4) Hyperbolic Functions
A hyperbolic function is an equation that contains x on the a y denominator of a fraction i.e. where a is a constant. x Examples are:
1 y x
- y 3 x 4 y 3x
Example 1
Draw the graph of y x y
-2
1 x -1
0
1
2
Example 1
Draw the graph of y
1 x NOTE: The special features of the hyperbola include:
The asymptotes
The branches
Example 2
Draw the graph of y x y
-2
2 x -1
0
1
2
Example 2
Draw the graph of y
2 x NOTE: The special features of the hyperbola include:
The asymptotes
The branches
Homework
Ex 12B p. 359 – 360 ALL
QUESTIONS
Due Tuesday
Exponential Growth and Decay
HSC 2008 Q25
Exponential Growth and Decay
HSC 2004 Q26
Homework
Ex 12C p. 364 – 365 ALL QUESTIONS
Due Friday
Your Cheat Sheets for AM4 and AM5 will be checked!
5) Direct Variation
This variation (also called direct proportionality) occurs when one variable follows another i.e. when one increases, so does the other. When one decreases, so does the other.
Direct variation problems can occur in the following ways:
a) y is directly proportional to x.
i.e. y x
b) y is directly proportional to the square of x.
c)
