h(t)=-4000t^2+3000t

Question

The height "h" of a fleas jump in millimeters can be modeled by the function h(t)=-4000t^2+3000t, where t is the time in seconds. What is the maximum height that the flea will reach? What time will it reach the max height?

Answer 1

Hi Maddie,

 

The function h(t) defines a parabola that opens downward. If we could find the y coordinate of the vertex, that value would be the max height of the flea.

 

For a quadratic function defined as ax² + bx + c, the axis of symmetry is the line x = -b/2a. One way to locate the vertex of a parabola is to determine the axis of symmetry and plug -b/2a into the function. 

 

See https://www.desmos.com/calculator/mowugqrqm8 .

 

The -b/2a evaluates to 3/8 = 0.375.

 

h(3/8) = 562.5 (which is the highest that flea will go!)