Question:
Given that a parabola intersects the x-axis at x=-4 and x=2, and intersects the y-axis at y=-16, find the equation of the parabola.
Solution:
Sketch of graph:
Now, there is a fast and slow method to this question. The slower method is to let 
The faster method is to let 
Why? We know that x=4 is a root of the polynomial, so it has a factor of (x-4). Similarly, the polynomial has a factor of (x-2). The constant k (to be determined) is added to scale the graph, so that the graph will satisfy y=-16 when x=0.
So, we just substitute in y=-16, x=0 into our new equation.
So 
In conclusion, the equation of the parabola is 
Singapore Maths Tuition 
This one is similar, using “parameter k” technique on more challenging problem:
http://tomcircle.wordpress.com/2013/05/06/generalized-analytic-geometry/
LikeLike