Question

an arch at a new amusement park is constructed with two vertical walls and a parabolic arch top, where x represents the horizontal distance in feet and f(x) represents the height in feet. the y - axis represents the vertical left edge of the arch. since the arch and its base are symmetrical, complete the equation for the line containing the vertical, right edge of the arch. x =

Explanation:

Step1: Identify symmetry property

The arch is symmetric about the vertical line passing through its vertex. The vertex is at $(30,45)$. The left - most point of the base is at $x = 0$ (left - edge of the arch represented by y - axis) and the right - most point of the base is at $x = 70$.

Step2: Determine right - edge equation

Since the arch is symmetric about $x = 30$ and the left - edge is at $x = 0$, the right - edge is at the same horizontal distance from the axis of symmetry as the left - edge. The distance from the left - edge ($x = 0$) to the axis of symmetry $x = 30$ is $30$ units. So, the right - edge is at $x=30 + 30=60$.

Answer:

$x = 60$