The given problem is already in the vertex form.
#color(blue)"The vertex form"#
#color(maroon)(y=a(x-h)^2+k)#
Where #(h,k)# is the vertex.
Our problem
#y=-2(x+1)^2+7#
#y=-2(x-(-1))^2+7#
#(h,k) = (-1,7)#
The vertex is #(-1,7)#
Intercepts on #x# and #y# axes occur where the curve crosses them.
To find #y# intercept we need to plug in #x=0#
#y=-2(0+1)^2+7#
#y=-2(1)+7#
#y=-2+7#
#y=5#
The #y-#intercept is #(0,5)#
For finding #x-#intercepts, we need to plug in #y=0#
#0=-2(x+1)^2+7#
Subtract #7# from both ends and isolating the term containing #x#
#-7 = -2(x+1)^2#
Let us rewrite it as #-2(x+1)^2=-7# It looks better to when the variable is kept of the left side of the equation.
#-2(x+1)^2=-7# dividing by #-2# on both sides isolates #(x+1)^2#
We get
#(x+1)^2=7/2#
Take square root on both the sides we get
#sqrt((x+1)^2) = +-sqrt(7/2)#
#x+1 = +-sqrt(7/2)#
Subtract #1# from both sides to solve for #x#
#x=-1+-sqrt(7/2)#
The #x-#intercepts are #(-1+sqrt(7/2))# and #(-1-sqrt(7/2))#
