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

1 Answer
Jun 5, 2015

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#