Answer
Please see the graph.
Vertex: $(0, -1)$
x-intercepts: -1/2, 1/2
y-intercepts: -1
Work Step by Step
$f(x)=4x^2-1$
$a=4$, $b=0$, $c=-1$
$x=-b/2a$ is the vertex.
$x=-b/2a$
$x=-0/2*4$
$x=0/8$
$x=0$
$f(x)=4x^2-1$
$f(0)=4*0^2-1$
$f(0)=4*0-1$
$f(0)=0-1$
$f(0)=-1$
$y=0$
$f(x)=4x^2-1$
$0=4x^2-1$
$0=(2x+1)(2x-1)$
$2x+1=0$
$2x+1-1=0-1$
$2x=-1$
$2x/2=-1/2$
$x=-1/2$
$2x-1=0$
$2x-1+1=0+1$
$2x=1$
$2x/2=1/2$
$x=1/2$
