Question 252853
The max height is at the vertex.

In order to find the vertex, we first need to find the t-coordinate of the vertex.

To find the t-coordinate of the vertex, use this formula: {{{t=(-b)/(2a)}}}.

From {{{h=-16t^2+30t+4}}}, we can see that {{{a=-16}}}, {{{b=30}}}, and {{{c=4}}}.

{{{t=(-(30))/(2(-16))}}} Plug in {{{a=-16}}} and {{{b=30}}}.

{{{t=(-30)/(-32)}}} Multiply 2 and {{{-16}}} to get {{{-32}}}.

{{{t=15/16}}} Reduce.

So the t-coordinate of the vertex is {{{t=15/16}}}.

Now that we know the t-coordinate of the vertex, we can use it to find the h-coordinate of the vertex.

{{{h=-16(15/16)^2+30(15/16)+4}}} Plug in {{{t=15/16}}}.

{{{h=-16(225/256)+30(15/16)+4}}} Square {{{15/16}}} to get {{{225/256}}}.

{{{h=-225/16+30(15/16)+4}}} Multiply {{{-16}}} and {{{225/256}}} to get {{{-225/16}}}.

{{{h=-225/16+225/8+4}}} Multiply {{{30}}} and {{{15/16}}} to get {{{225/8}}}.

{{{h=289/16}}} Combine like terms.

So the h-coordinate of the vertex is {{{h=289/16}}}.

So the vertex is *[Tex \LARGE \left(\frac{15}{16},\frac{289}{16}\right)].

This means that the max height is {{{h=289/16}}} which is {{{h=18.0625}}} feet.