SPM 2011 Additional Mathematics (Paper 1, Question 5)

The diagram above shows the graph of a polynomial function

, where

is a constant (whose value is controlled by the vertical

-slider). When

, we have a quadratic curve:

Can you name the equation associated with the axis of symmetry (shown in red) of the curve? [Hint: the equation of the axis symmetry is related to the location at which the -axis is cut by the red line.]
Use vertical -slider to explore the change in positions of (the red dot) and (the blue dot). Does the change in the value of changes the absolute positions of these two points (what about their relative positions?)
The line shown in green is a line which connects and . Can you write down the equation of the green line?
A right-angle triangle is formed when the red/green/blue lines intersect each other. Can you compute the area of the right-angle triangle, ?

Write down an expression to denote the area of the triangle in the general case for other values of

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