A landscape architect is designing a curved retaining wall for a corporate campus. The wall follows a horizontal parabolic path modeled by the equation $x = -{}2(y - 6)^2 + 15$. Which of the following equations represents the axis of symmetry for this retaining wall?

An aerospace technician is verifying the dimensions of a horizontal parabolic cooling vent. The vent's shape is modeled by the equation $x = (y - 15)^2 + 25$. The technician identifies the axis of symmetry as the horizontal line $y = \_\_\_\_$.

A robotic systems engineer is programming a robotic arm to follow a horizontal parabolic path. To ensure the arm's reference line is correctly set, match each mathematical model or characteristic of the path with its corresponding representation of the axis of symmetry.

Geometric Alignment in Landscape Design

In a quality control department, a technician is inspecting a part with a horizontal parabolic edge modeled by the equation $x = ay^2 + by + c$. To verify the part's symmetry, the technician uses the formula y = -rac{b}{2a} to calculate the axis of symmetry. Is this formula correct for the given equation?

Determining the Center Line for a Parabolic Tool Path

A CNC machine programmer is writing a Standard Operating Procedure (SOP) on how to locate the center reference line (the axis of symmetry) of a horizontal parabolic tool path. Arrange the steps in the correct order to recall the standard mathematical procedure for finding this axis when the path is given in the general form $x = ay^2 + by + c$.