The UV index on a sunny day can be modeled by the function f(x)=-0.15(x-13)^2+7.6 where x represents the time of day on a 24-h clock and f(x) represents the UV index. At what time(s) was the UV index 7? (2 marks)

Answer 1

- 0.15 ( x - 13 ) ^ 2 + 7.6 = 7 Subtract 7.6 to both sides

- 0.15 ( x - 13 ) ^ 2 + 7.6 - 7.6 = 7 - 7.6

- 0.15 ( x - 13 ) ^ 2 = - 0.6 Divide both sides by - 0.15

( x - 13 ) ^ 2 = - 0.6 / - 0.15

( x - 13 ) ^ 2 = 4 Take square root to both sides

x - 13 = + OR - 2 Add 13 to both sides

x - 13 + 13 = + OR - 2 + 13

x = + OR - 2 + 13

The solutions are :

x = - 2 + 13 = 11

and

x = 2 + 13 = 15