Question

martha is designing an arch that will stand in front of city hall. this function describes the archs height, in feet, above the ground x feet from one end of the arch:
$y = -1.125(x - 4)^2 + 18$
what is the maximum height of the arch?
______ feet

Explanation:

Step1: Identify the function form

The given function is in vertex form \( y = a(x - h)^2 + k \), where \((h, k)\) is the vertex of the parabola. Here, \( a=-1.125 \), \( h = 4 \), and \( k = 18 \).

Step2: Determine the maximum/minimum

Since \( a=-1.125<0 \), the parabola opens downward, so the vertex represents the maximum point. The \( y \)-coordinate of the vertex (\( k \)) gives the maximum value of the function.

Answer:

18