Question

How to write an equation for a rational function with: x intercepts at x = 6 and x = 5?

Answer 1

Start from the factored form to find

`f(x) = x^2 - 11x + 30`

Explanation:

An `x` intercept occurs when `f(x) = 0`. Then, we are just looking for a rational function `f(x)` such that `f(6) = f(5) = 0`. We can easily construct a polynomial with the desired property by starting in factored form.

It should be clear that if `f(x) = (x-6)(x-5)` that plugging in `5` or `6` will give `0`. Then, as a polynomial is certainly a rational function, it satisfies the desired requirements, and so we can just expand to get

`f(x) = x^2 - 11x + 30`