Question

How do find the vertex and axis of symmetry, and intercepts for a quadratic equation `f(x)=-4x^2`?

Answer 1

The vertex form of a quadratic equation is
`color(white)("XXXX")` `f(x) = m(x-a)^2+b`
`color(white)("XXXX")` `color(white)("XXXX")`with vertex at `(x,f(x)) =(a,b)`
Since`f(x) = -4x^2` can be written
`color(white)("XXXX")` `f(x) = -4(x-0)^2+0`
it has a vertex at `(x,f(x)) = (0,0)`

`f(x)= -4x^2` is a parabola which opens downward with an axis of symmetry as vertical line through the vertex.
That is, the axis of symmetry is `x=0`