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.
Sketch of graph:
Now, there is a fast and slow method to this question. The slower method is to let , and solve 3 simultaneous equations.
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.
In conclusion, the equation of the parabola is .