Answer:
39 feet
Step-by-step explanation:
The equation of the path of the book is an upside down parabola.
We can find the x-coordinate of the vertical axis.
The x-coordinate of the maximum point is
x = -b/2a
for a parabola written in the following form
f(x) = ax² + bx + c
We have -16t² + 24t + 30, so we have
a = -16
b = 24
c = 30
t = -b/2a = -24/(2 × (-16)) = -24/(-32) = 0.75
The maximum height occurs at time = 0.75 seconds.
Now we plug in the time into the equation to find the maximum height.
h(x) = -16t² + 24t + 30
h(0.75) = -16(0.75)² + 24(0.75) + 30
h(0.75) = -9 + 18 + 30
h(0.75) = 39
Answer: 39 feet
