Question

What are the `x` and `y` intercepts of the curve `3x^2-x+8=0`?

Answer 1

There is no `x`-intercept and `y`-intercept is at `(0,6)`.

Explanation:

For `x`-intercept put `y=f(x)=0` i.e. `3x^2-x+6=0`

but as discriminant is `b^2-4ac=(-1)^2-4xx3xx6=-71`, we do not have a real solution and hence there is no `x`-intercept. Also observe that `3x^2-x+6=3(x-1/6)^2+71/12` and hence for all values of `x`, `3x^2-x+6>0` and hence no `x`-intercept.

For `y`-intercept, we should put `x=0` and then `y=f(0)=6` and `y`-intercept is at `(0,6)`
graph{3x^2-x+6 [-20, 20, -2, 18]}