Answer:
about 19.94 ft
Step-by-step explanation:
It is convenient to start with a parabola that opens downward and has a width of ±1 and a height of 1. Its equation is ...
f(x) = 1 - x²
To make it have a horizontal width of ±45 feet, we need to use a horizontal expansion factor. The equation is then ...
g(x) = f(x/45) = 1 - (x/45)²
To make it have a height of 16 when x=20, we need a vertical expansion factor.
h(x) = a·g(x) = a(1 -(x/45)²)
Filling in the given values, we can find the value of the vertical expansion factor, a:
16 = a(1 -(20/45)²) = a(1 -(4/9)²)
16 = a(65/81)
16(81/65) = a = 19 61/65 ≈ 19.94 . . . . . . . . divide by the coefficient of "a"
This makes the equation of the arch be ...
h(x) = 19.94(1 -(x/45)²)
At the tallest point, x = 0, so the arch is ...
h(0) = 19.94(1 -0) = 19.94 . . . . feet high
