Question

I am a parent trying help my son, who has trouble understanding and remembering how to work his math. I never had this math, so it is hard for me to explain it. If I see it worked out. Then I can explain it, (I, Think) here is the problems. A ball is tossed into the air and it is modeled by the function h(t)=-16t^2+96t+8. This has a maximum height of? Also need to find the time it would return to the ground?

Answer 1

Your dealing with parabolas and quadratic equations.
If you have never learned this, I don't see how you can help him.
He must know how to find the vertex of the above parabola, either by completing the square or a short formula which he must memorize.

h(t) = -16t^2 + 96t + 8
= -16(t^2 - 6t + ......) + 8
= -16(t^2 - 6t <b>+ 9 - 9 </b>) + 8
= -16( (t-3)^2 - 9) + 8
= -16(t-3)^2 + 144 + 8
= -16(t-3)^2 + 152
the vertex is (3,152)

so the maximum height is 152 ft, after 3 seconds

when it hits the ground h(t) = 0
0 = -16t^2 + 96t + 8
divide by -8
2t^2- 12t - 1 = 0
by the formula ...
t = (12 ± √152)/4
= 6.0822 or a negative t, which makes no sense

It will take appr 6.08 seconds to return to the ground.

Answer 2

WHOOOUUUU