f(x) = -(x+3)²+4
Vertex form:
y = a(x - h)² + k
where (h, k) is the vertex
f(x) has the vertex form with h = -3 and k = 4, then the vertex is (-3,4)
To find the x-intercept, we have to find the x-values that makes f(x) = 0.
0 = -(x+3)²+4
-4 = -(x+3)²
(-4)/(-1) = (x+3)²
√4 = x + 3
√4 has two results 2 and -2, then:
2 = x + 3
2 - 3 = x
-1 = x
-2 = x + 3
-2 - 3 = x
-5 = x
Therefore, the x-intercepts are (-5,0) and (-1, 0)