Question

What is the axis of symmetry of the function f(x) =-(x+9)(x-21)

Answer 1

x = 6

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
`-(b)/(2a)`

Here, a = -1 b = 12

`-(b)/(2a)\\\\=-(12)/(2\cdot(-1))\\\\=-(-6)\\\\=6`

Therefore, the axis of symmetry is x = 6

Answer 2

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