Algebra 2 Word Problem. I would be grateful for an answer with an explanation.

Question

A golfer, standing on the second deck at a driving range, hits a golf ball 40 feet above the ground with an initial vertical velocity of 160 feet per second. The function h(t)=-16t^2+160t+40 represents the height h (in feet) of the golf ball after t seconds. Find the maximum height the ball reaches.

Answer 1

You first have to find what t is

Using the formula: t=-b/2a (think back to the quadratic equation, what a, b and c stand for, that's where you are getting a and b from.

t=-160/2(-16)=-160/-32=t=5 So you know from this equation that the ball will reach it's peak in 5 seconds. Now you can substitute 5 in for t in the original function h(t)=-16t^2+160t+40  to get the maximum height.

h(5)=-16(5)^2+160(5)+40

h(5)=-16(25)+800+40

h(5)=-400+840

h(5)=440

The ball will reach a maximum height of 440 ft.