Answer:
7) y = -6x^2 + 60x
a. -6x^2 + 60x = 0
-6x(x - 10) = 0
x = 10 seconds
b. The highest point occurs at 5 seconds.
-6(5^2) + 60(5) = -150 + 300 = 150 feet
c. -6x^2 + 60x = 96
-6x^2 + 60x - 96 = 0
6x^2 - 60x + 96 = 0
x^2 - 10x + 16 = 0
(x - 2)(x - 8) = 0
x = 2 seconds, 8 seconds
8) y = -3x^2 + 18x
a. -3x^2 + 18x = 0
-3x(x - 6) = 0
x = 6 seconds
b. The highest point occurs at 3 seconds.
-3(3^2) + 18(3) = -27 + 54 = 27 feet
c. -3x^2 + 18x = 24
-3x^2 + 18x - 24 = 0
3x^2 - 18x + 24 = 0
x^2 - 6x + 8 = 0
(x - 2)(x - 4) = 0
x = 2 seconds, 4 seconds