Question

What is the vertex form of # f(x) = -x^2 -x-2 #?

Answer 1

The vertex form of equation is `f(x) = - (x+ 0.5)^2 -1.75`

Explanation:

`f(x)= - x^2-x-2 = - (x^2 +x) -2 = - (x^2 +x +(1/2)^2) +1/4-2`

`f(x)= - (x +1/2)^2 -7/4 or f(x) = - (x+ 0.5)^2 -1.75`

Comparing with general vertex form of equation,

`f(x) = a(x-h)^2+k ; (h,k)` being vertex, here vertex is at `(-0.5 , -1.75)`

The vertex form of equation is `f(x) = - (x+ 0.5)^2 -1.75` [Ans]