Name: Dylan Kirkwood
Who is asking: Other
Level: Secondary

How can you factor a quadratic equation by graphing it?

Hi Dylan,

Lets look at the problem the other way arount first. Suppose

y = x2 - x - 6 = (x + 2)(x - 3)

Knowing the factors helps to graph the equation since you can see immediately that when x = -2, y = 0 and when x = 3, y = 0. Thus you know two points on the graph, (-2,0) and (3,0).

There is a theorem, called the Factor Theorem which says that this process works the other way around. That is if you graph

y = x2 - x - 6

and realize that (-2,0) and (3,0) are points on the graph then you can conclude that (x - 2) and (x + 3) are factors of x2 - x - 6. This Factor Theorem is true for more than quadratics, it says that: If f(x) is a polynomial and f(a) = 0 then (x - a) is a factor of f(x).

Go to Math Central