Question 1054211
Convert to vertex form by completing the square,
{{{h=-16t^2+8t+48}}}
{{{h=-16(t^2-(1/2)t)+48}}
{{{h=-16(t^2-(1/2)t+1/16)+48+16(1/16)}}}
{{{h=-16(t-1/4)^2+49}}}
So the max height of {{{49}}} occurs when {{{t=1/4}}}{{{s}}}.