Question

The law f(t) = -t2 + 6t + 15 represents the number of kilometers of congestion, as a function of time, registered in a city. With that, determine the maximum number of congestion in that city and the maximum time to reach this value.

Answer 1

t = 3

24 km of congestion.

Explanation:

To find the maximum time, we want to know the coordinates of the vertex of the parabola. To get the x-value of the vertex, we would do -b/2a. In this case, a = -1 and b = 6. So, we will have -(6) / 2 * (-1) = -6 / -2 = 6 / 2 = 3.

To get the y-value of the vertex, just substitute the 3 whenever it says "t".

f(3) = -(3)^2 + 6 * (3) + 15 = -9 + 18 + 15 = 9 + 15 = 24

So, the maximum time it takes to reach the value is t = 3, and the maximum number of congestion in the city will be 24 km.

Hope this helps!

Answer 2

Maximum Congestion: 24

Maximum Time to reach Congestion: 3

Explanation:

Easiest and fastest way is to graph the equation and analyze the graph for it's maximum vertex.