A manufacturing technician is programming a robotic welder to follow a horizontal parabolic path. The path is modeled by the equation $x = (y - 8)^2 + 15$, where the coordinates represent inches from a reference point. What are the coordinates of the vertex for this welder's path?

In technical fields such as HVAC design and satellite communications, horizontal parabolas are used to model airflow and signal reflection. To work with these shapes, technicians must recall how to identify their 'turning point,' or vertex. Match each term or equation below with the correct description of its role in finding the vertex of a horizontal parabola.

An HVAC technician is modeling the airflow through a horizontal parabolic duct using the general form equation $x = ay^2 + by + c$. True or False: The technician can find the $y$-coordinate of the vertex for this duct by using the formula $y = -\frac{b}{2a}$.

A fabrication technician is analyzing the curve of a custom-machined part modeled by the horizontal parabolic equation $x = ay^2 + by + c$. To locate the vertex (the turning point) of this curve for precision cutting, the technician must follow a specific set of steps. Arrange the following steps in the correct order to determine the vertex coordinates.

Determining Vertex Coordinates for a Horizontal Parabolic Reflector