| \ A
B * - - * (a,b)
| b| \
| | \
- - + - - * - * - -
O a C 2\
The line has the equation: .
If , then: .
The area of the rectangle is: .
ii) What is the possible value(s) of , so that the rectangle exists?
On the graph, we see that can range from 0 to 2.
The graph of: is a parabola. iii) Sketch the graph of
It opens downward and has x-intercepts at 0 and 2.
The graph looks like this:
| * *
| * *
- - * - - - - - - - * - - a
iv) Find the maximum value of and the value of for which this occurs.
The maximum value of the parabola occurs at its vertex.
The vertex is at
. . and: .