jmc

Question

Ben is climbing a tree with a lot of branches. His height off the ground at time t is 2t^2-5t+29 feet. To the nearest foot, what will his minimum height be?

Accepted Answer

Completing the square, we get align* 2t^2 - 5t + 29 &= 2 ( t^2 - 52 t ) + 29 &= 2 [ ( t - 54 )^2 - 5^24^2 ] + 29 &= 2 ( t - 54 )^2 + 2078. align*Thus, the minimum height is 2078. To the nearest integer, this is 26.