Answer
Vertex: $(1, 4)$
Opens downward
x-intercepts: 0, 2
y-intercept: 0
Work Step by Step
$f(x)=-4x^2+8x$
$y=-4x^2+8x$
$y=-4(x^2-2x)$
$y-4*(-2/2)^2=-4(x^2-2x)+4*(-2/2)^2$
$y-4*(-1)^2=-4(x^2-2x)+4*(-1)^2$
$y-4*1=-4(x^2-2x)+4*1$
$y-4=-4(x^2-2x+1)$
$y-4=-4(x-1)^2$
$y-4+4=-4(x-1)^2+4$
$y=-4(x-1)^2+4$
Vertex: $(1, 4)$
Opens downward
$x=0$
$f(x)=-4x^2+8x$
$f(0)=-4*0^2+8*0$
$f(0)=-4*0+0$
$f(0)=0+0$
$f(0)=0$
$y=0$
$y=-4(x-1)^2+4$
$0=-4(x-1)^2+4$
$0-4=-4(x-1)^2+4-4$
$-4=-4(x-1)^2$
$-4/-4=-4(x-1)^2/-4$
$1=(x-1)^2$
$\sqrt 1=\sqrt{(x-1)^2}$
$±1 = x-1$
$1=x-1$
$1+1=x-1+1$
$2=x$
$-1=x-1$
$-1+1=x-1+1$
$0=x$
x-intercepts: 0, 2
y-intercept: 0
