You did not post what you already know about this exercise, so I do not really know where to begin helping you.
I also do not know what level of physics information they associate with exercises like this one within your school's grade 11 courses. (Maybe you are studying physics, maybe you are studying math, maybe you are studying both. Maybe you are studying regression techniques for fitting data points to a curve. Quadratic equations arise in all of these subjects. I have no way of knowing what you're doing unless you tell me.)
So, I'll guess.
I guess that you're not studying quadratic regression.
I also guess that you're not learning about the physics involved (such as the effect of gravity, the initial velocity, the fact that air resistance may be ignored), so you don't need to derive any formulas.
Therefore -- in addition to the given data that you posted -- you also need to have been told by somebody that the following equation is a model that relates the elapsed time and the height above the ground of this ball from the point in time when it's released until it hits the ground 1.25 seconds later.
h = At^2 + Bt + C
where the symbol h is the height variable and the symbol t is the elapsed-time variable. The symbols A, B, and C are the parameters whose values you need to find.
You've been given six pairs of related t and h values. Do you notice that some of the pairs are identical? You need to use three different pairs to write a system of equations.
If you take these three pairs of h and t values and substitute them into the quadratic model above, then you will get three different equations containing the symbols A, B, and C. Have you learned anything about how to solve a system of three equations?
If you know what's coming up in this approach, then you would start with the data pair that says h is 5 when t is 0. (Starting with the point where t = 0 simplifies the problem, as you will hopefully see in a moment.)
Substitute h = 5 and t = 0 into the quadratic model below.
h = At^2 + Bt + C
5 = A(0^2) + B(0) + C
What do you discover?
Can you use this discovery to simplify the rest of the problem to a system of two equations in A and B?
You're told that h is 0 when t is 1.25
You're told that h is 9 when t is 0.5.
This is enough information to write those two last equations. Solve that system to find the values of A and B.
If you get stuck, then please let me know what you already know, and show whatever work you can accomplish, and I'll continue from there.
(FYI: A, B, and C are all integers.)
