A simple task, we throw a ball into the air upwards as vertically as possible and record the height of the ball at release, $(height=1m, time = 0)$, and the time the ball hit the ground. $(height=0, time=2.80s)$.
We are trying to solve the equation of the height/time parabola using transformations between standard, vertex, and factored form.
I am not exactly sure where to begin, any help would be appreciated.
(I guess we need to find out the speed of the ball when it was released, how high the ball went and at what time, (vertex))
Set the origin at the point of release, and let the initial velocity be $u$
First use $s=ut+\frac 12 at^2$ with $s=-1,t=2.8,a=-9.8$ to get $u$
Then use $v^2=u^2+2as$ with $v=0$ to get the max height $s$ above the point of projection.
Can you finish?