A manufacturing technician is programming a robotic cutter to follow a parabolic path on a metal sheet. The path is defined by the coordinate equation $x = -2(y+3)^2 + 2$. According to the standard form of a horizontal parabola, what is the vertex of this path?

A fabrication technician is programming a high-precision laser cutter to follow a parabolic path defined by the coordinate equation $x = -2(y+3)^2 + 2$. Match each geometric property of the laser's path with its correct mathematical value or description.

Axis of Symmetry in Structural Design

A technical designer is mapping a curved machinery component defined by the coordinate equation $x = -2(y+3)^2 + 2$. To ensure the component is manufactured accurately, the designer must follow a specific sequence of steps to graph the path. Arrange the following steps in the correct order as they would be performed to graph this horizontal parabola.

A manufacturing technician is analyzing a curved cut on a metal sheet defined by the coordinate equation $x = -2(y+3)^2 + 2$. True or False: This parabolic path opens to the right (toward the positive $x$-axis).

A manufacturing apprentice is programming a CNC milling machine to carve a curved groove onto a steel plate. The curved path is modeled by the horizontal parabola equation $x = -2(y+3)^2 + 2$. To ensure the plate is aligned correctly on the workbench, the apprentice needs to identify which direction the curve bends. Because the lead coefficient $a$ is negative, this horizontal parabola opens to the ____.

CNC Toolpath Calibration and Setup