Question 1188443


{{{h = -2t^2 + 7t + 9}}}, where {{{h}}} is height, in metres, and {{{t }}}is time, in seconds.

Find the maximum height reached by the stone.
since you have a parabola that opens downward, maximum will be at vertex
so, rewrite equation in vertx form by completing square

{{{h=(-2t^2 + 7t) + 9}}}......factor out {{{-2}}}
{{{h=-2(t^2 - (7/2)t) + 9}}}
{{{h=-2(t^2 - (7/2)t+b^2) -(-2b^2)+ 9}}}.............{{{b=(7/2)/2=7/4)}}}
{{{h=-2(t^2 - (7/2)t+(7/4)^2) +2(7/4)^2+ 9}}}
{{{h=-2(t - 7/4)^2 +2(49/16)+ 9}}}
{{{h=-2(t - 7/4)^2 +121/8}}}

=> vertex is at (7/4,121/8)

so, the maximum height reached by the stone is {{{h=121/8}}} or {{{h=15.125}}}

How many seconds does it take to reach the maximum height?

{{{h = -2t^2 + 7t + 9}}}....plug in {{{h=15.125}}}
{{{15.125 = -2t^2 + 7t + 9}}}........solve for {{{t}}}
{{{2t^2 - 7t + 6.125 = 0}}}.....using quadratic formula we get
{{{t=1.75}}}seconds

How many seconds does it take for the stone to reach the water?

{{{0 = -2t^2 + 7t + 9}}}....plug in {{{h=0}}}
{{{0 = -2t^2 + 7t + 9}}}......factor
{{{0 = -(t + 1) (2t - 9)}}}

solutions:
{{{t = -1}}}-> disregard negative time
{{{t = 9/2}}}
{{{t = 4.5}}}
it takes {{{4.5}}}seconds  for the stone to reach the water