Answer:
[tex]Vertex = (-2,-25)[/tex]
Step-by-step explanation:
Given
[tex]f(x) = (x - 3)(x + 7)[/tex]
Required
The vertex
[tex]f(x) = (x - 3)(x + 7)[/tex]
Open bracket
[tex]f(x) = x^2 -3x+7x-21[/tex]
[tex]f(x) = x^2 +4x-21[/tex]
Express -21 as 4 - 25
[tex]f(x) = x^2 +4x+4-25[/tex]
Group as:
[tex]f(x) = (x^2 +4x+4)-25[/tex]
Factorize the expression in bracket
[tex]f(x) = (x+2)^2-25[/tex]
The vertex form is:
[tex]f(x) = a(x - h)^2 + k[/tex]
Where the vertex is:
[tex]Vertex = (h,k)[/tex]
[tex]Vertex = (-2,-25)[/tex]
