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Verified Answer :

syed514

f(x) =-(x+9)(x-21)

Manipulating algebrically,
We get,
f(x) =-(x+9)(x-21)
      = -(x^2 -21x + 9x - 189)
      = -(x^2 -12x - 189)
      = -x^2 + 12x + 189
Axis of symmetry = -b/2a
plugging the values,
x = -12/-2
   = 6

SociometricStar

Answer:

x = 6

Step-by-step explanation:

The given equation is \(f(x)=-(x+9)(x-21)\)

We write the equation in standard form of parabola \(f(x)=ax^2+bx+c\) using FOIL

\(f(x)=-(x+9)(x-21)\\\\f(x)=-(x^2-21x+9x-189)\\\\f(x)=-x^2+12x+189\)

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 \(-\frac{b}{2a}\)

Here, a = -1 b = 12

\(-\frac{b}{2a}\\\\=-\frac{12}{2\cdot(-1)}\\\\=-(-6)\\\\=6\)

Therefore, the axis of symmetry is x = 6

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