A construction site manager is reviewing a blueprint that includes a horizontal parabolic support beam modeled by the equation $x = ay^2 + by + c$. If the manager notes that the coefficient $a$ is negative, in which direction does the beam's curve open?

An industrial designer uses the horizontal parabolic equations $x = ay^2 + by + c$ and $x = a(y - k)^2 + h$ to model curved surfaces in architectural plans. Match the sign of the coefficient $a$ with its corresponding orientation.

A technician is installing a parabolic heat shield modeled by the horizontal equation $x = a(y - k)^2 + h$. If the leading coefficient $a$ is positive, the shield's curve will open toward the ____.

Determining Horizontal Parabola Orientation

A landscape designer is mapping out a curved garden path that follows the horizontal parabola equation $x = ay^2 + by + c$. True or False: If the leading coefficient $a$ is a positive value ($a > 0$), the curve of the path will open toward the right.