a What is the distance from the diver to the diving board when the diver is still on it? Does the diver's height above water at that time correspond to the height of the diving board?
B
b What does the y-coordinate of the vertex represent? How can you find it?
a The height of the diving board above the water is 1 meter.
B
b The maximum height reached by the diver is 3.25 meters above water.
C
c The diver is ascending from 0 meters to 0.5 meters, and descending from 0.5 meters until hitting the water, which is achieved approximately at 1.1 meters from the diving board.
Practice makes perfect
a When the diver is still on the diving board, the distance to it is 0. To find the height of the diving board we must evaluate x=0 into f(x)=-9x^2+9x+1.
The maximum height reached by the diver is 3.25 meters above water.
c Since the leading coefficient of f(x)=-9x^2+9x+1 is negative (-9), the parabola must open downward. This means that, from left to right it goes up until the vertex, and then goes down.
Thus, the diver is ascending from x=0 to the x-coordinate of the vertex which is, according to part B, x= 12. Consequently, after x=0.5 meters the diver is descending until hitting the water.
From the graph above, we can see that the diver entered the water 1.1 meters away from the diving board.
