Question 161504
Note: I'm replacing "s" with "y" and "t" with "x" to get the equation {{{y=-16x^2+64x+25}}}


To answers questions C and D, we need to find the vertex. Remember, the vertex represents the highest/lowest point.




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=-16x^2+64x+25}}}, we can see that {{{a=-16}}}, {{{b=64}}}, and {{{c=25}}}.



{{{x=(-(64))/(2(-16))}}} Plug in {{{a=-16}}} and {{{b=64}}}.



{{{x=(-64)/(-32)}}} Multiply 2 and {{{-16}}} to get {{{-32}}}.



{{{x=2}}} Divide.



So the x-coordinate of the vertex is {{{x=2}}}. Note: this means that the axis of symmetry is also {{{x=2}}}.



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



{{{y=-16x^2+64x+25}}} Start with the given equation.



{{{y=-16(2)^2+64(2)+25}}} Plug in {{{x=2}}}.



{{{y=-16(4)+64(2)+25}}} Square {{{2}}} to get {{{4}}}.



{{{y=-64+64(2)+25}}} Multiply {{{-16}}} and {{{4}}} to get {{{-64}}}.



{{{y=-64+128+25}}} Multiply {{{64}}} and {{{2}}} to get {{{128}}}.



{{{y=89}}} Combine like terms.



So the y-coordinate of the vertex is {{{y=89}}}.



So the vertex is *[Tex \LARGE \left(2,89\right)].



Since the vertex is *[Tex \LARGE \left(2,89\right)], this means that {{{x=2}}} and {{{y=89}}}. 



So at 2 seconds, the object is at the highest point of 89 feet.