Question

State the axis of symmetry of f(x)=-(1)/(2)x^(2)+3

Answer 1

`f(x)=-(1)/(2)x^2+3`

The axis of symmetry is located at the x-coordinate of vertex of the function. For a function of the form:

`f(x)=ax^2+bx+c`

The coordinates of its vertex V(h,k) are given by:

`\begin{gathered} h=-(b)/(2a) \\ where \\ a=-(1)/(2) \\ b=0 \\ so\colon \\ h=-(0)/(2(-(1)/(2)))=0 \end{gathered}`

Therefore, the axis of symmetry is located at:

`x=0`