Hwa Chong IP Sec 2 Maths Question – Equation of Parabola

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:

maths-tutor-parabola

Now, there is a fast and slow method to this question. The slower method is to let y=ax^2+bx+c, and solve 3 simultaneous equations.

The faster method is to let y=k(x+4)(x-2).

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.

-16=k(4)(-2).

-16=-8k.

So k=2.

In conclusion, the equation of the parabola is y=2(x+4)(x-2).