Function notation and graphs of quadratics

Question

Nasa launches a rocket at t=0 seconds. It's height, in meters above sea level, as a function of time is given by h(t)=-4.9t^2+226t+262. Give at least 2 decimal places in answer.

Assuming the rocket will splash down in the ocean, at what time does splash occur?

Rocket splashes down after how many seconds?

How high above sea level does the rocket get is peak?

Answer 1

To find time to splashdown, set h(t)=0 and solve for t using the quadratic formula. You will get a negative and a positive solution. Since time starts at t=0, the positive solution is the correct one.

The peak height is at the vertex of the height-vs.-time parabola, which is at

t = -b/(2a) = -226 / [2(-4.9)] sec = ? sec

Plug this value of t into h(t) to get h_max. You should be able to finish from here.