Question

Determine the minimum or maximum of the value. What is this value?

Answer 1

`\text{\textbf{Minimum,}}V(-(5)/(2),(11)/(2))`

1) Since this quadratic equation has an "a" coefficient, the leading one, greater than 0. We can state that this quadratic has a minimum value described by the Vertex of that Parabola.

2) So, we are going to use the following formula to find the Vertex Coordinates:

`\begin{gathered} h=-(b)/(2a) \\ h=(-10)/(2(2))=(-10)/(4)=(-5)/(2)=-(5)/(2) \end{gathered}`

And now we need to plug that h-coordinate into the quadratic formula to get the "k" coordinate:

`\begin{gathered} k=y=2x^2+10x+18 \\ k=2(-(5)/(2))^2+10(-(5)/(2))+18 \\ k=(11)/(2) \end{gathered}`

And that's the answer: Minimum, V(-5/2,11/2)