Question

What is the x-intercept of `f(x) = (x-3)^2 - 5`?

Answer 1

`x` intercepts of the function are `3-sqrt5` and `3+sqrt5`

Explanation:

`x`-intercept of the function `f(x)=(x−3)^2−5` will be given by the value of `x` for which the function's value is `0`.

The function expands to `x^2-6x+4` and this will be `0` for the x-intercept;

and intercepts on `x`-axis, using quadratic formula will be given by

`x=(6+-sqrt(6^2-4*1*4))/2`

or `(6+-sqrt20)/2` or `3+-sqrt5`

Hence `x` intercepts of the function are `3-sqrt5` and `3+sqrt5`