Answer
Vertex: $(-1/2, -4)$
Opens upward
x-intercepts: -3/2, ½
y-intercept: -3
Work Step by Step
$f(x)=4x^2+4x-3$
$y=4x^2+4x-3$
$y+3=4x^2+4x-3+3$
$y+3=4x^2+4x$
$y+3=4(x^2+x)$
$y+3+4(1/2)^2=4(x^2+x+(1/2)^2)$
$y+3+4(1/4) =4(x^2+x+1/4) $
$y+3+1 =4(x^2+x+1/4) $
$y+4 =4(x +1/2)^2 $
$y+4-4 =4(x +1/2)^2-4$
$y=4(x +1/2)^2-4$
Vertex: $(-1/2, -4)$
Opens upward
$x=0$
$f(x)=4x^2+4x-3$
$f(0)=4*0^2+4*0-3$
$f(0)=4*0+0-3$
$f(0)=0-3$
$f(0)=-3$
$y=0$
$y=4(x +1/2)^2-4$
$0=4(x +1/2)^2-4$
$0+4=4(x +1/2)^2-4+4$
$4=4(x +1/2)^2$
$4/4=4(x +1/2)^2/4$
$1=(x +1/2)^2$
$\sqrt 1 =\sqrt {(x +1/2)^2}$
$±1 = x+1/2$
$-1=x+1/2$
$-1-1/2 =x+1/2-1/2$
$-3/2 =x$
$1=x+1/2$
$1-1/2=x+1/2-1/2$
$1/2=x$
x-intercepts: -3/2, ½
y-intercept: -3
