Added by Tony B
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))