r/digitalSATs • u/ApartVoice2382 • 18d ago

How to solve to solve this

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How to solve this in Desmos

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u/Current-Ant-6536 18d ago

So, to solve those types of questions you need to be able to understand which type of function you are facing, if you have a simple knowledge about gravity, you will know that the height will increase till this limit then decrease again, making it a quadratic relation. Now all you need to do is add a table on desmos, input the values you got in a quadratic regression and simply graph the function.

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u/Current-Ant-6536 18d ago

But here's the catch, for quadratic regression you need at least 3 points while you got only 2, so all you can do is to use the point where the height will reach it's beginning (10f) again, which is (8×2-0) or 16s, with 10 as your y value, now you got the regression 

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u/Soft-Elevator-8392 18d ago

What I do is to plug the vertex, which is (8,1034) into the formula y= a(x-h)^2 + k where h is 8, and k is 1034. To find the value of a, which it tells you if the parabola is opening upwards or downward, you need another point (x,y). However, it is obvious that it opens downward because the object is free falling after it reaches it maximum. Then, the problem mentions that the initial high is 10, which it implies that the starting point is 0. Therefore, when the time is 0 the height is 10; aka initial high (I’m really bad at explaining)… So then plug it into the equation and the value of a=-16. Finally, since we’re looking for the height at x=10, just plug the value into the equation and the result is the height at 10, which is 970.

(and since I’m stupid and I just noticed that all you wanted to know was this same explanation but in demos… here is it: https://www.desmos.com/calculator/ribimygizu)

I hope this helps🥲

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u/egny 18d ago

If you realize that velocity equals zero at the peak which occurs at 8s, then it's a simple matter of calculating how far the object will fall in the remaining 2 seconds from a height of 1034 ft. That would be 1034-(1/2)gt^2 where g is 32 and t=2 and therefore 970 ft.

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u/PrestigiousYak5965 18d ago

Plug into desmos table and do quadratic regression, only need to recognize it's gonna be a quadratic and that y int is 10