Answer:
The axis of symmetry is x=6.
Step-by-step explanation:
The given function is
\(f(x)=-(x+9)(x-21)\)
Using distributive property, we get
\(f(x)=-(x^2-21x+9x-189)\)
\(f(x)=-x^2+12x+189\) .... (1)
If a quadratic function is defined as
\(y=ax^2+bx+c\) .... (2)
then the axis of symmetry is defined as
\(x=\frac{-b}{2a}\)
On comparing (1) and (2), we get
\(a=-1,b=12,c=189\)
The axis of symmetry of given function is
\(x=\frac{-12}{2(-1)}=6\)
Therefore the axis of symmetry is x=6.
