If an arch has the equation h=-0.06d^2+2.13 and each end at the same level, how wide is the arch to the nearest metre?

Question

Grade 10- parabolas

Answer 1

This is a parabolic arch. When h=0 (zero height), 0.06d^2=2.13 so d=±√(2.13/0.06)=±√35.5=±5.96m. The positive and negative values are the right and left extremes of the arch, presumably where the arch meets the upright walls on either side. Therefore the width of the arch is 5.96-(-5.96)=11.92 or 12m to the nearest metre.