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.

A design technician is mapping a horizontal parabolic curve for a new architectural element. To find the $x$-intercept of the curve—the point where it crosses the horizontal axis—the technician must substitute the value ____ for the variable $y$ in the equation.

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.