Question

Find the vertex of the graph of the quadratic function and determine whether it's an absolute maximum or an absolute minimum: y = x2 + 18x + 83.

Answer 1

The function:

y = x² + 18x + 83

follows the general form:

y = ax² + bx + c

The x-coordinate of the vertex is found as follows:

$\begin{gathered} x_V=\frac{-b}{2a} \\ x_V=\frac{-18}{2\cdot1} \\ x_V=-9 \end{gathered}$

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