h= -4.9t^2+ 56t
Since the coefficient of t^2 is a negative number, the parabola will open downwards. Therefore, the maximum value of this equation will occur at the vertex.
The vertex of a parabola is the point (- b2 a,h(- b2 a)), where a and b are coefficients of t^2 and t. Let's substitute -4.9 for a and 56 for b to find the first coordinate of the vertex.
We found that the maximum height the rocket will reach is 160 meters.
b In Part A we found that the point where the rocket's height has maximum value occurs at the vertex, ( 407,160). Since time is the first coordinate in this point, the rocket will reach its maximum height 407 seconds after it is launched. Let's use a calculator to write this number in decimal form.
