Question

Diver jumps from a rock into lake 25ft. Trajectory is described by
h(x)=-1.5x^2+4x+25.
Find Maximum height the diver reaches. How should I start this problem? THx

Answer 1

Well pretend that it is a graph. The maximum height would be the maximum Y value. This graph is obviously a parabola so the maximum value will be at the vertex. Since the front x is negative, the parabola will open downwards.

To find the vertex of a parabola in standard polynomial form you use to formula -b/2a to find the x coordinate of the vertex(Where a is the coefficient on the first term and b is the coefficient on the second term; in our case a and b equal -1.5 and 4 respectively). therefore the x coordinate of the vertex is 4/3. To find the y cordinate we have to plug this into the original function. Therefore the y coordinate is 85/3. Thus our answer is

85/3