a arrow is shot upward the height of the arrow is determined by y=64x-8x^2 where x is the time in seconds and y is the height in feet

Question

anonymous · Answer

what is the height of the arrow after 3 seonds? after 6 seconds?
how long did it take to reach the maximum height?
what is the maximum height?
when did the arrow hit the ground?
determine a reasonable domain and range that represents this situation

campbell_st · Answer

ok... for the 1st part substitute x = 3 into the equation  
        then x = 6 into the equation. 


max height.... the curve is a parabola and the max height is on the line of symmetry 

and can be found using 

$$x = \frac{-b}{2a}$$

in your equation b = 64 and a = -8 

when you have a time value for the max height, substitute to to get the max height

and when does the arrow hit the ground

solve 

$$64x - 8x^2 = 0$$

one value will be 0 the other is the time when it hits the  ground... 


the domain is from x = 0 to when it hits the ground

the range is from 0 to the max height

hope this helps