Answer:
Vertex = (-1,4).
Step-by-step explanation:
Given equation is [tex]y=-(x-1)(x+3)[/tex].
Now we need to find the vertex of the graph of given function [tex]y=-(x-1)(x+3)[/tex].
To find that we can rewrite given function into vertex form
[tex]y=-(x-1)(x+3)[/tex]
[tex]y=-(x^2+3x-1x-3)[/tex]
[tex]y=-(x^2+2x-3)[/tex]
[tex]y=-(x^2+2x+1-1-3)[/tex]
[tex]y=-((x+1)^2-1-3)[/tex]
[tex]y=-((x+1)^2-4)[/tex]
[tex]y=-(x+1)^2+4[/tex]
Now compar this equation with [tex]y=a(x-h)^2+k[/tex]
we get: h=-1, k=4
Hence vertex is (h,k) or (-1,4).
