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# help

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A ball is thrown into the air from the roof of a building that is 25 metres high. The ball reaches a maximum height of 45 metres above the ground after 2 seconds. Determine the equation of the quadratic in standard form.

Jan 16, 2020

#1
+108771
+2

The easiest way, if you understand what you are doing is to say the top of the buliding is the point (0,0)

later the whole graph will be translated up 25m.

So the parabola goes through (0,0)  (4,0) and (2,20)

$$h=k(t)(t-4)\\ sub\; in (2,20)\\ 20=2k*-2\\ 20=-4k\\ k=-5\\ h=-5t(t-4)\\ h=-5t^2+20t\\ \text{now translate it up 25 metres and I have}\\ h=-5t^2+20t+25$$

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Jan 16, 2020

#1
+108771
+2

The easiest way, if you understand what you are doing is to say the top of the buliding is the point (0,0)

later the whole graph will be translated up 25m.

So the parabola goes through (0,0)  (4,0) and (2,20)

$$h=k(t)(t-4)\\ sub\; in (2,20)\\ 20=2k*-2\\ 20=-4k\\ k=-5\\ h=-5t(t-4)\\ h=-5t^2+20t\\ \text{now translate it up 25 metres and I have}\\ h=-5t^2+20t+25$$

Melody Jan 16, 2020