Question

Determine whether there is a minimum or maximum value to the quadratic function.f(x) = 2x2 − 18x + 6 Find the minimum or maximum value of f.Find the axis of symmetry.

Answer 1

`f(x)=2x^2-18x+6`

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:

`(h,k)=((-b)/(2a),f(-(b)/(2a)))`

then, for the function given

`\begin{gathered} h=-((-18))/(2(2)) \\ h=(18)/(4)=4.5 \\ \\ k=2(4.5)^2-18(4.5)+6 \\ k=-34.5 \end{gathered}`

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