Question

What is the vertex, axis of symmetry, the maximum or minimum value, and the range of parabola `f(x) = −4(x − 8)^2 + 3`?

Answer 1

`f(x)=-4(x-8)^2+3`
is a standard quadratic in vertex form:
`f(x) = m(x-a)^2+b`
where `(a,b)` is the vertex.

The fact that `m=-4<0` indicates that the parabola opens downward (the vertex is a maximum value)

The vertex is at `(8,3)`

Since it is a standard position parabola, the axis of symmetry is
`x=8`

The maximum value is `3`

The Range of `f(x)` is `(-oo,+3]`