A structural engineering firm is designing a parabolic reflector for a satellite dish. The profile of the reflector is modeled by the equation $x = 2y^2 + 12y + 17$. To ensure precise alignment of the receiver, a technician needs to identify the specific geometric properties of this curve based on its standard form $x = 2(y + 3)^2 - 1$. Match each property to its correct value or description.

In a precision engineering task, a technician is modeling a curved structural component using the equation $x = 2y^2 + 12y + 17$. To identify the component's turning point, the equation must be converted into the standard form $x = a(y - k)^2 + h$ by completing the square. Arrange the following steps in the correct chronological order to perform this conversion as described in the technical manual.

In a precision manufacturing layout, a technician is analyzing the horizontal parabolic path of a robotic arm modeled by the equation ${}x = 2(y + 3)^2 - 1$. Based on this standard form equation, what are the coordinates of the vertex?

In a technical design for a parabolic antenna, the curvature is modeled by the equation $x = 2(y + 3)^2 - 1$. Based on this equation, the parabola opens to the right.

A CAD designer is mapping out the parabolic curve of a solar reflector component using the standard form equation $x = 2(y + 3)^2 - 1$. To align the support bracket directly along the center of the curve, the designer needs to identify the axis of symmetry. This axis of symmetry is located at the horizontal line $y =$ ____.

CNC Machine Path Programming: Completing the Square

Solar Collector Curve Verification