Answer:
[tex]y=(x-6)^2+4[/tex]
Step-by-step explanation:
Vertex Form Of The Parabola
The equation of a parabola can be expressed in either standard or vertex form. The standard form is
[tex]y=ax^2+bx+c[/tex]
and the vertex form is
[tex]y=a(x-h)^2+k[/tex]
Where (h,k) it the vertex of the parabola
Transforming one into the other form is easily achieved by applying simple algebra .
Our function is
[tex]y=x^2-12x+40[/tex]
Completing squares, we have
[tex]y=x^2-12x+36+40-36[/tex]
Reducing
[tex]\boxed{y=(x-6)^2+4 }[/tex]
The vertex of the parabola is the point (6,4)
