find the max height

Question

A diver jumps from a rock 30 meters high into a lake below. His trajectory is described by the function h(x) = -2x^2 + 4x + 30, where h(x) is the height in meters after x seconds. Find the maximum height the diver reaches.

Answer 1

To find the max height, you have to find the vertex. The x coordinate is found by:

x = -b/(2a)

x = -4/(2*-2)

x=1

Now, plug this into the original equation to find the y coordinate, which will be the max height.

h(1)=-2(1)² + 4(1) + 30

h = 32 meters