Question

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

Answer 1

$\text{\textbf{Minimum,}}V(-\frac{5}{2},\frac{11}{2})$

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:

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

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

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

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