algebra question

Question

a golf ball is chipped into the air from a small hill with an upward velocity of 50ft/s. it’s height h in feet after t seconds is given by the function h=-16t^2+50t*10. how long will it take the ball to reach the maximum height? what is the maximum height the ball reaches? what is a reasonable domain and range?

Answer 1

Thank you for posting your question!

When you have a quadratic function like this the optimal value is going to happen at the vertex, so you want to find that by taking

t = -b/2a = -50 / (2*-16) = -50 / -32 = 1.5625 seconds

To get the maximum height then you want to plug that value back into the original function

h(1.5625) = -16(1.5625)^2 + 50(1.5626) + 10

=-39.0625 + 78.125 + 10

=49.0625 feet

For domain and range you just want to think in terms of values that are possible … so since domain is a unit of time it can’t be less than 0, which means that the range cannot be below 10. I hope that helps! :)