in order to determine if a quadratic function has a minimum or maximum if the coefficient of the square term is positive, the function has a minimum. If the coefficient of the square term is negative the function has a maximum.
In this case, the function has a minimum value because 2 is a positive value.
The minimum value and the axis of symmetry can be found at the vertex, which can be found through the formula:
[tex](h,k)=(\frac{-b}{2a},f(-\frac{b}{2a}))[/tex]then, for the function given
[tex]\begin{gathered} h=-\frac{(-18)}{2(2)} \\ h=\frac{18}{4}=4.5 \\ \\ k=2(4.5)^2-18(4.5)+6 \\ k=-34.5 \end{gathered}[/tex]Answer:
The function has a minimum value located at (4.5,-34.5)
The axis of symmetry of any quadratic function is situated in the x-coordinate of the vertex, the axis of symmetry for the given function is x=4.5
