Question

2 more

Answer 1

@eraserlaser

Answer 2

First one
Part A: We know we can find the roots of functions by using the quadratic formula or reverse foiling(Assuming you know how to FOIL). I've done the calculations and it comes out to t = 1 and t = -5. The meaning of the x or t intercept of the function is where the sandbag starts at (t = -5) and where it it lands(t = 1). We can calculate this by plugging in the t values in your f(t) function.
Part B: I do not see any f(x) function, I'm not really sure what the question is asking.... Sorry
Part C: We need Part B.....

Answer 3

ok thats fine

Answer 4

Second one
Part A: Easy you are given a function H(t) that represents the height of an object at a given time. We need to find an equation that will only have height dependent on time. All we need to do is plug the value of v (60ft/s) (velocity of the object) and s (100ft) (feet above the ground) in the the function H(t).
Part B: You need to find the vertex using the vertex formula, for all intensive purposes I'll post the short cut instead of deriving the whole equation (-b/(2a)) where y = ax^2 + bx +c and you can find this by looking at our H(t) function that we found in part A (a = -16) (b = 60) we plug our equation (-b/(2a)) into our H(t) function and we get the maximum height.
Part C: We make a table of t, g(t) and H(t) and pick like 5 points as our values of t (ie. 1, 0 or something in a low number range). To find where they equal just set the two equations equal to each other and solve for t and plot that point on our table as well.
Part D: If we id Part C correctly then we should have a couple values of t and a couple values of H(t) and g(t), now see where the H(t) and g(t) values are going while there getting close to the intercept (H(t) = g(t)) which means if H(t) and g(t) are going down then the projectile is going down and vice-versa if its going up.
I also notice in problem 1 you need to use the vertex form of a quadratic equation which is y = a(x-h)^2 + k, I can calculate it if you want but if you are given this problem you should have been taught this already (also I don't really want to take the time and calculate it lol :p)
I put a drawing of the table for Part C:
Hope this helps a little.