Answer
(a) $(-2,-25)$
(b) $(-7,0),(3,0)$
(c) $(-4,-21),(0,-21)$
(d) see graph.
Work Step by Step
Given $f(x)=x^2+4x-21=(x+2)^2-25$, we have:
(a) the vertex is $(-2,-25)$
(b) for x-intercepts, solve $f(x)=0$ to get $(-7,0),(3,0)$
(c) for $f(x)=-21$, we have $x^2+4x-21=-21$, thus $x=-4,0$ or $(-4,-21),(0,-21)$
(d) see graph.