Question

How do you write `f(x) = 1 − 6x − x^2` into vertex form?

Answer 1

Vertex form of equation is `f(x)= - (x+3)^2 +10`

Explanation:

`f(x) = -x^2-6x+1 =-(x^2+6x) +1 = -(x^2+6x+ 9) +9 +1` or

`f(x)= - (x+3)^2 +10` . Comparing with standard vertex form of equation `f(x) =a (x-h)^2 +k ; (h,k)`being vertex, we get vertex is at `(-3, 10)`

Vertex form of equation is `f(x)= - (x+3)^2 +10` [Ans]

Answer 2

Vertex (-3, 10)

Explanation:

`f(x) = - x^2 - 6x + 1`
x-coordinate of vertex:
`x = -b/(2a) = 6/-2 = -3`
y-coordinate of vertex. Substitute x by -3 into f(x).
`f(-3) = - 9 + 18 + 1 = 10`
Vertex (-3, 10)