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