An architectural designer is modeling a curved support beam that follows the path of a horizontal parabola. To find the $x$-intercept of the beam—the point where it crosses the horizontal $x$-axis—which algebraic step should the designer perform first in the equation?

A technician at a solar energy company is calibrating a horizontal parabolic trough modeled by an algebraic equation. To find the $y$-intercepts of this horizontal parabola, the technician should substitute ${}0$ for $y$ in the equation and solve for $x$.

A quality control technician is verifying the alignment of a horizontal parabolic reflector on a coordinate grid. To document the component's exact position, the technician must identify the intercepts. Match each type of intercept with the correct algebraic procedure used to find it.

Locating Vertical Intercepts for Parabolic Structural Elements

Drafting Manual: Identifying Parabolic Intercepts

A manufacturing technician is programming a computerized CNC router to cut a custom parabolic-shaped slot along a horizontal metal template. The path is modeled by a horizontal parabola with the equation $x = ay^2 + by + c$. To find the vertical entry points ($y$-intercepts) where the router crosses the reference axis, the technician must follow a standard verification procedure. Arrange the steps of this procedure in the correct order to find the $y$-intercepts of this horizontal parabola.