Velvet Rope - Parabolas

Question

A parabola is formed by a piece of velvet rope found around a museum display. This parabola can be modeled by the graph of the function y= 4/225x² — 16/15x + 40 where x and y are measured in inches and y represents the number of inches the parabola is above the ground. How far above the ground is the lowest point on the rope?

Answer 1

Vertex at x = -b / 2a

x = (16/15) / (8 / 225)

x = (15/16) / 225 / 8)

x = 30

Determine f(30).