MATH QUESTION - involving parabolas?

Question

The arch can be modeled by the function

h= -0.06d2 (the 2 is an exponent) + 2.13
h meteres is the height of the arch, d metres is the horizontal distance from the center of the arch

b) if the ends of the arch are level of the river, how wide is the arch, to the nearest metre?
c) at a horizontal distance of 2 m from one end of the arch, how high is the arch, to the nearest tenth of a metre?

Answer 1

For (b), to find the width, we need to set the height (h) equal to 0 and solve the equation for the horizontal distance (d):

0 = -0.06d^2 + 2.13
0.06d^2 = 2.13
d^2 = 35.5
d = 5.96 m

So from the center of the arch to the end, the distance is 5.96 m. Thus, the width of the arch is twice this, or 11.92 m.

To find the height of the arch 2 m from the end, we can use the formula now that we know where the end is. Since the end is at 5.96 m, the height we're looking at is at 3.96 m:

h = -0.06d^2 + 2.13
h = -0.06(3.96 m)^2 + 2.13
h = 1.19 m