Answer
Vertex: $(1/2, 5/4)$
Opens downward
x-intercepts: 0, 1
y-intercept: 0
Work Step by Step
$f(x)=-5x^2+5x$
Vertex: $x=-b/2a$
$x=-5/2*(-5)$
$x=-5/-10$
$x=1/2$
$f(x)=-5x^2+5x$
$f(1/2)=-5(1/2)^2+5*1/2$
$f(1/2)=-5*1/4+5/2$
$f(1/2)=-5/4+5/2$
$f(1/2)=5/4$
Vertex: $(1/2, 5/4)$
Opens downward
$x=0$
$f(x)=-5x^2+5x$
$f(0)=-5*0^2+5*0$
$f(0)=-5*0+0$
$f(0)=0+0$
$f(0)=0$
$y=0$
$f(x)=-5x^2+5x$
$0=-5x^2+5x$
$0=-5x(x-1)$
$-5x=0$
$-5x/-5=0/-5$
$x=0$
$x-1=0$
$x-1+1=0+1$
$x=1$
x-intercepts: 0, 1
y-intercept: 0
