A manufacturing technician is evaluating a curved metal component whose profile is modeled by the equation $x = -4(y+2)^2 + 4$. To ensure the piece is positioned correctly in the assembly, match each geometric property of this parabola with its corresponding value or description.

A precision machinist is programming a CNC router to cut a metal component with a parabolic profile defined by the equation $x = -4(y+2)^2 + 4$. To set the machine's reference point at the peak of the curve, the machinist must identify the vertex. What are the coordinates of the vertex (h, k) for this profile?

An automotive engineer is designing a parabolic reflector whose profile is modeled by the equation $x = -4(y+2)^2 + 4$. Because the leading coefficient $a$ is negative, the engineer determines that the reflector opens toward the ____.

A quality control technician is verifying the dimensions of a structural bracket whose profile follows the equation $x = -4(y+2)^2 + 4$. True or False: The $x$-intercept for this bracket's profile is located at the point $({}-12, 0)$.

Identifying the Axis of Symmetry for a Parabolic Blueprint

A machinist is drafting a standard operating procedure (SOP) to map out a parabolic mold defined by the equation $x = -4(y+2)^2 + 4$. Arrange the following steps in the correct order to accurately recall and apply the procedure for determining the properties and graphing this specific horizontal parabola.

Drafting a Technical Specification for a Custom Curved Component