Question

What are the vertex, axis of symmetry, maximum or minimum value, domain, and range of the function, and x and y intercepts for `f(x)= x^2-10x`?

Answer 1

`f(x) =x^2-10x`
is the equation of a parabola with a normal orientation (the axis of symmetry is a vertical line) which opens upward (since the coefficient of `x^2` is not negative)

rewriting in slope-vertex form:
`f(x) = (x^2-10x+25)-25`

`= (1)(x-5)^2 -25`

The vertex is at `(5,-25)`

The axis of symmetry pass through the vertex as a vertical line:
`x=5`

From the opening comments we know `(-25)` is the minimum value.

The Domain is `{xepsilonRR}`

The Range is `{f(x) epsilon RR | f(x)>= -25}`