Question

If a function of the form `y=ax^2+k` has an `x`-intercept of 7.5, what is the other `x`-intercept?

Answer 1

Other `x`-intercept is `-7.5`

Explanation:

`x`-intercept appears where`y=0` and hence is given by

`ax^2+k=0` i.e. `k=-ax^2`

When `x=7.5`, we have `k==-axx7.5^2=-(225a)/4`

i.e. `ax^2-(225a)/4=0`

or dividing by `a`, `x^2-225/4=0`

i.e. `x^2-(15/2)^2=0`

or `(x-15/2)(x+15/2)=0`

Hence intercepts are given by `x=15/2=7.5` and `x=-15/2=-7.5`