Answer:
x = 6
Step-by-step explanation:
The given equation is [tex]f(x)=-(x+9)(x-21)[/tex]
We write the equation in standard form of parabola [tex]f(x)=ax^2+bx+c[/tex] using FOIL
[tex]f(x)=-(x+9)(x-21)\\\\f(x)=-(x^2-21x+9x-189)\\\\f(x)=-x^2+12x+189[/tex]
Now, we know that the axis of symmetry passes through the vertex. Hence, in order to find the vertex of the parabola, we find the x coordinate of the vertex.
x coordinate of the vertex is [tex]-\frac{b}{2a}[/tex]
Here, a = -1 b = 12
[tex]-\frac{b}{2a}\\\\=-\frac{12}{2\cdot(-1)}\\\\=-(-6)\\\\=6[/tex]
Therefore, the axis of symmetry is x = 6
