Question

What is the vertex, axis of symmetry, the maximum or minimum value, and the range of parabola `f(x)=x^2 -2x -15`?

Answer 1

You can factorise: `=(x+3)(x-5)`

Explanation:

This gives you the zero-points `x=-3andx=5`
Halfway between these lies the axis of symmetry :
`x=(-3+5)//2->x=+1`
The vertex is on this axis, so putting in `x=1`:
`f(1)=1^2-2.1-15=-16`
So the vertex `=(1,-16)`
Since the coefficient of `x^2` is positive, this is a minumum
There is no maximum, so the range is `-16<=f(x)< oo`
Since there are no roots or fractions involved the domain of `x` is unlimited.
graph{x^2-2x-15 [-41.1, 41.1, -20.55, 20.52]}