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a small rocket is fired into the air from the ground. It reaches its highest point, 108 meters at 4.7 seconds.?
I need to know
three points that the graph goes through
the graphing window that allows you to see these points
vertex coordinates of the parabola
an equation in vertex form that fits the three known points
Lastly the h (3) and a real world meaning for this value
The only 3 points we know are the initial (0,0), the peak (vertex) (4.7,108), and the final (by symmetry) (9.4,0). To find the equation, we start with the standard parabola formula:
h(t) = at² + bt + c
Since h(0)=0, then c=0.
We know that h(9.4)=0, so:
(0) = a(9.4)² + b(9.4)
b = -9.4a
We also know that h(4.7)=108, so we have:
(108) = a(4.7)² + b(4.7)
4.7a + b = 22.98
Now combine equations to find a:
4.7a + (-9.4a) = 22.98
a = -4.889
b = -9.4(-4.889) = 45.96
So equation of rocket's flight is:
h(t) = -4.889t² + 45.96t (std. form)
h(t) = -4.889(t - 4.7)² + 108 (vertex form)
h(3) = 93.9 ft
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