Question 1177994


{{{h= -16t^2 + 16t + 96}}}

 the highest point that Erika reached is the vertex, so write equation in vertex form

{{{h= -16t^2 + 16t + 96}}}......complete square

{{{h= (-16t^2 + 16t) + 96}}}......factor out {{{-16}}}

{{{h= -16(t^2 - t) + 96}}}

{{{h= -16(t^2 - t+b^2)-(-16)b^2 + 96}}}....coefficient of {{{t}}} is {{{1}}}, so {{{b=1/2}}}


{{{h= -16(t^2 - t+(1/2)^2) +16(1/2)^2 + 96}}}

{{{h= -16(t - 1/2)^2 +16(1/4) + 96}}}

{{{h= -16(t - 1/2)^2 +4 + 96}}}

{{{h= -16(t - 1/2)^2 +100}}} 


=> vertex is at ({{{1/2}}},{{{100}}})

so, the highest point that Erika reached is {{{100}}} feet