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Algebra 2 math homework?
The height, h, in feet, a ball will reach thrown in the air is a function of time, t, in seconds, given by the equation h(t)= -16t^2 +30t + 6. Find to the nearest tenth, the maximum height, in feet, the ball will reach.
Please show work and explain. Thanks.
1 Answer
- Anonymous1 decade agoFavorite Answer
this function is a simple parabola (bowl shaped graph, reveres direction once) your looking for the highest point on that parabola, which will be the highest possible y for an given value of x.
http://hotmath.com/hotmath_help/topics/vertex-of-a...
theres allitle more info and a good animated graph.
anyway your problem is in standard format
y = ax2 + bx + c = h(t)= -16t^2 +30t + 6
for my work, y is h and x is t
now to find the x part of the vertex, you use -b/2a
-b/2a = -30/-32= 15/16= 0.9375
now plug that in for x to find y in the original equation
-16(15/16)^2+30(15/16)+6
now do the math (or program your graphics calculator to do it for you) and you get
Y=20.0625=20+1/16 or 321/16
so the vertex (or highest point on the graph) to the neerest tenth is:
(.9,20)
and the answer to your problem is
20 (rounded)