Using Excel, I get a quadratic of
This has an R^2 of .9994. Which is pretty dang good.
Plug in x=7 to find the height at 7 seconds. I get 2.3
It hits the ground when y=0. That occurs when x=7.96 seconds.
I'm doing this math course through correspondence and really the only indication they've given to determine a quadratic function is that the first difference numbers are not constant, while the second difference numbers are constant (same #). Well I'm stuck on this question because it doesn't follow the above rule, plus aren't the points always at the same distance on both sides of the parabola (mirrored)?
Question A says 'confirm' that it is quadratic though, so I'm wondering if it really is, so could someone explain WHY it is, if it is?
Well no where in the explanations or examples did they show how to form an equation from the chart or turn it into a graph...this is the first unit so maybe I'm not there yet. Like I said in the original post, it just covers the first and second differences. In all four examples given, the second differences were the same number...that's why I'm confused.
I don't know much about this subject but form what I understand the second derivative of a quadratic is constant but the method of second difference is a numerical approximation of the derivative (so there is bound to be variations). I think what you're looking for is a fairly constant second difference and linear relationship in with first differences.
Out of interest have you been taught to use technology to solve these problems or have you been taught to do them using graphical method. I plotted a graph of the first differences to get an approximations of the linear equation that relates them then integrated and I got an answer similar to what galactus posted.
Bobak
Go here and download the program and install it.
1)Click F4 to insert a point series. And insert all these points.
2)Right click on the left where it says "Series 1" and select "Insert Tredline".
3)Click on polynomial and set the order be 2, then click okay.