Question

Let t=0 correspond to 1994. Average total government health care spending per person from 1994 to 2000 is estimated by the following equation where h is in dollars and t is years between 0 and 6:
h=429+29t-t^2
Find the vertex of the parabola. What is the meaning of the y-intercept of the graph?

Answer 1

The vertex of a parabola will occur where the derivative of the parabola equation is 0.

h=429+29t-t^2
h' = 29 - 2t

29 - 2t = 0 => 2t = 29 => t = 14.5.

Thus, the parabola of the vertex is at t=14.5. We can solve for the y coordinate using this: 429 + 29(14.5) - 14.5^2 = 639.25.

Since the y-intercept occurs at t = 0, in this parabola the y-intercept represents the spending per person at year t = 0, or 1994.

Answer 2

amazing.. we have not even learned how to get from 429+29t-t^2 -> 29-2t.. i cant even remember what it is called but i remember learning it last semester..
thank you.