Answer
Vertex: $(0,5)$
x-intercepts: $(-1, 0)$, $(1,0)$
y-intercept: $(0,5)$
Work Step by Step
$f(x) = -5x^2+5$
$a=-5$, $b=0$, $c=5$
Vertex is at $x=-b/2a$
$x=-0/2*-5$
$x=0/-10$
$x=0$
$x=0$
$f(x) = -5x^2+5$
$f(0) = -5*0^2+5$
$f(0)=-5*0+5$
$f(0)=0+5$
$f(0)=5$
$(0,5)$ is the vertex and the y-intercept.
$y=0$
$f(x) = -5x^2+5$
$0 = -5x^2+5$
$0-5=-5x^2+5-5$
$-5=-5x^2$
$-5/-5 =-5x^2/-5$
$1 =x^2$
$\sqrt 1 =\sqrt {x^2}$
$±1 =x$
$x=-1$
$f(x) = -5x^2+5$
$f(-1) = -5(-1)^2+5$
$f(-1) =-5*1+5$
$f(-1) =-5+5$
$f(-1)=0$
$x=1$
$f(x) = -5x^2+5$
$f(1) = -5(1)^2+5$
$f(1) =-5*1+5$
$f(1) =-5+5$
$f(1)=0$
$(-1,0)$ and $(1,0)$ are the x-intercepts of the graph.
