The height of an object, h(t), is determined by the formula
h(t) = –16t2 + 256t, where t is time, in seconds. Will the object reach a maximum or a minimum? Explain or show your reasoning.
I have trouble with questions like this when the value of the variable is not given.
How can I find the answer without having to graph the given function?
Using symmetry, the t-coordinate of the turning point lies half-way between the t-intercepts. Do you know how to find it. Once you have the t-coordinate of the turnng point, how to get the h-coordinate shuld be clear. And it's a negative parabola (coefficient of squared term is negative). So the turning point is a maximum.
You should recognise that h(t) is a parabola opening downwards, and hence this has a maximum. Also you should know that the maximum occurs midway between the roots, which in this case are obvious.