Question 165101
Remember, the max height occurs at the vertex. So if we find the y-coordinate of the vertex, we find the max height.


Note: the same applies to the min height (if there exists a min height)




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=-0.0032x^2+x+3}}}, we can see that {{{a=1}}}, {{{b=1}}}, and {{{c=3}}}.



{{{x=(-(1))/(2(-0.0032))}}} Plug in {{{a=-0.0032}}} and {{{b=1}}}.



{{{x=(-1)/(-0.0064)}}} Multiply.



{{{x=156.25}}} Divide



So the x-coordinate of the vertex is {{{x=156.25}}}.




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



{{{y=-0.0032x^2+x+3}}} Start with the given equation.



{{{y=-0.0032(156.25)^2+156.25+3}}} Plug in {{{x=156.25}}}.



{{{y=-0.0032(24414.0625)+156.25+3}}} Square {{{156.25}}} to get {{{24414.0625}}}.



{{{y=-78.125+156.25+3}}} Multiply



{{{y=81.125}}} Combine like terms.



So the y-coordinate of the vertex is {{{y=81.125}}}.



So the vertex is (156.25,81.125).



Since the y-coordinate is {{{y=81.125}}}, this means that the max height is 81.125 ft.