The function:
y = x² + 18x + 83
follows the general form:
y = ax² + bx + c
The x-coordinate of the vertex is found as follows:
[tex]\begin{gathered} x_V=\frac{-b}{2a} \\ x_V=\frac{-18}{2\cdot1} \\ x_V=-9 \end{gathered}[/tex]The y-coordinate is found replacing Xv into the equation, as follows:
Yv = (-9)² + 18(-9) + 83
Yv = 81 - 162 + 83
Yv = 2
The vertex is located at (-9, 2)
Given that a = 1 is positive, then the vertex is a minimum
