Question 149392
a) correct

b) correct

c)


To find the max height, we need to find the vertex.





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



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



{{{x=(-b)/(2a)}}} Start with the given formula.



From {{{y=-16t^2+32t+256}}}, we can see that {{{a=-16}}}, {{{b=32}}}, and {{{c=256}}}.



{{{x=(-(32))/(2(-16))}}} Plug in {{{a=-16}}} and {{{b=32}}}.



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



{{{x=1}}} Divide.



So the x-coordinate of the vertex is {{{x=1}}}. Note: this means that the axis of symmetry is also {{{x=1}}}.



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



{{{y=-16t^2+32t+256}}} Start with the given equation.



{{{y=-16t^2+32t+256}}} Plug in {{{x=1}}}.



{{{y=-16t^2+32t+256}}} Start with the given equation.



{{{y=-16(1)^2+32(1)+256}}} Plug in {{{t=1}}}.



{{{y=-16(1)+32(1)+256}}} Square {{{1}}} to get {{{1}}}.



{{{y=-16+32(1)+256}}} Multiply {{{-16}}} and {{{1}}} to get {{{-16}}}.



{{{y=-16+32+256}}} Multiply {{{32}}} and {{{1}}} to get {{{32}}}.



{{{y=272}}} Combine like terms.



So the y-coordinate of the vertex is {{{y=272}}}.



So the vertex is *[Tex \LARGE \left(1,272\right)].



So the highest point on the graph of {{{y=-16t^2+32t+256}}} is *[Tex \LARGE \left(1,272\right)].



This means that maximum height of the stone is 272 feet 



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From the previous solution, the highest point is at the point *[Tex \LARGE \left(1,272\right)]. So when t=1, then h=272. So the stone reaches the highest point at 1 second



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e) correct.