Question

can anyone help me with this problem?

Answer 1

h = -5t^2 + ut + h0
Initial height h0 = 6
h = -5t^2 + ut + 6
First step: Complete the square on the right. Keep u as a variable without putting in any numerical value yet because in the second part of the question they have a few different u values.

Answer 2

When you complete the square, the formula for the height will look something like this:
h = a(t - p)^2 + q

In this form we can quickly determine the maximum height because (p,q) will be the vertex and so the maximum height will be q.