Explanation:
h(x) = -(x + 11)² + 1
1.
the "zeroes" of a function are the values of x that create 0 as result.
so,
0 = -(x + 11)² + 1
(x + 11)² = 1
x + 11 = ±1 | as (+1)² = (-1)² = 1
x + 11 = 1
x = -10
x + 11 = -1
x = -12
smaller x = -12
larger x = -10
2.
the vertex of the parabola can be seen directly in the vertex form of the parabola equation, as it was given to us :
y = a(x - h) + k
(h, k) is the vertex.
so, in our case,
the vertex = (-11, 1)